I'd give a lot/the world/anything to know ... ( fam) → darei moltissimo/tutto l'oro del mondo/non so che cosa per sapere... fig: = betray) → verraten ( to sb an jdn); to give the game or show away (inf)→ alles verraten; to give oneself away→ sich verraten Note: I'm not certain if those sentences are completely grammatical however I am certain that they come up in conversation. So whether or not they are grammatical might not even be a good question.

The part - that gives human the capability of ... - is a Relative clause and the antecedent of the relative clause is the Noun - appliance. The gap inside the relative clause is marked by the "___", is actually the subject position. The antecedent is clearly the subject of the relative clause. So whenever the gap of the relative clause denotes a subject position of the relative clause, the relative elements ( e.g who, which etc) or subordinator ( e.g that) is not omitted. Can you give me something for the pain? → هَلْ يـُمْكِنُكَ إِعْطائِي شَيْئاً لِتَخْفيفِ الَأَلَمِ؟ → Můžete mi dát něco proti bolesti? → Kan jeg få noget mod smerten → Können Sie mir ein Schmerzmittel geben? → Μπορείτε να μου δώσετε κάτι για τον πόνο; → ¿Puede darme algo para el dolor? → Voitteko antaa jotakin kipuun? → Vous pouvez me donner quelque chose pour la douleur ? → Možete li mi dati nešto protiv bolova? → Mi può dare qualcosa per il dolore? → 痛み止めに何かもらえますか？ → 진통제 좀 주시겠어요? → Kunt u me iets voor de pijn geven? → Kan du gi meg noe mot smertene? → Czy może mi Pandać coś przeciwbólowego? → O senhor pode me dar alguma coisa para a dor → Вы не могли бы мне дать что-то обезболивающее? → Kan ni ge mig något smärtstillande? → คุณให้อะไรฉันสักอย่างเพื่อแก้ปวดได้ไหม? → Ağrı kesici bir şey verebilir misiniz? → Bạn có thể cho tôi thuốc giảm đau không? → 能给我开一点止疼药吗？ This sentence beginning is not grammatical. The word "gives" is a verb and consequently cannot modify a noun (appliance). You must either use a participial phrase (a phrase that begins with a verb form and behaves as an adjective) or an adjectival clause (a mini-sentence that behaves as an adjective.It is clear from context that "driving to work" describes "I" since "watermelons" typically do not drive. Can you give me a lift to the garage? (UK) → هَلْ يـُمْكِنُ أَنْ تُوَصِّلَني إِلى وَرَشَةِ للسَيَّاراتِ؟ → Můžete mě zavést do autoopravny? → Kan De give mig et lift til værkstedet? → Können Sie mich zur Autowerkstatt bringen? → Μπορείτε να με πάτε στο συνεργείο; → ¿Podría acercarme al taller? → Voitteko antaa kyydin korjaamolle? → Vous pouvez m'emmener au garage ? → Možete li me prebaciti do garaže? → Può darmi un passaggio all'autofficina? → 自動車修理工場まで私を乗せていってもらえますか？ → 정비소까지 태워 주시겠어요? → Kunt u me een lift naar de garage geven? → Kan du gi meg skyss til verkstedet? → Czy mógłby mnie Panpodwieźć do warsztatu? → O senhor pode me dar uma carona até a oficina mecânica? → Вы не могли бы подвезти меня до автомастерской? → Kan ni skjutsa mig till bilverkstaden? → คุณช่วยพาฉันไปที่อู่ได้ไหม? → Beni tamirciye kadar götürebilir misiniz? → Bạn có thể cho tôi đi nhờ đến chỗ sửa xe không? → 我能搭您的车去修车行吗？

to give sth for sth (= pay)→ etw für etw ausgeben; (= sacrifice)→ etw für etw (her) geben; (= exchange)→ etw gegen etw tauschen; what will you give me for it?→ was gibst du mir dafür?; how much did you give for it?→ wie viel hast du dafür bezahlt? a. ( gen) → dare; ( as gift) → regalare, dare (in dono); ( description, promise, surprise) → fare; ( particulars) → dare, fornire; ( decision) → annunciare; ( title, honour) → conferire, dare; ( assign, job) → assegnare, dare; ( dedicate, life, time) → consacrare, dedicare The predicator (FUNCTION), realized by the verb (WORD CLASS) - think, can license a Preposition Phrase (PP) as its complement - here, of an appliance giving human the capability of .... Inside the PP structure there is a head Preposition - here, of - and the complement of the head Preposition is a Gerund-Participle clause - here, an appliance giving human the capability of .... In your case the Gerund-Participle clause has an explicit subject - an appliance. Both of these are grammatical and mean the same thing as far as I can tell. However, I believe that the first choice is better in almost all circumstances. This is due to a possible ambiguity that the participial phrase could have. It is not uncommon (in spoken English at least) for participial phrases at the end of a sentence to modify the subject of the sentence rather than the noun they follow. For example, take the following sentence.

to give way to something→ von etw abgelöst werden; tears gave way to smiles→ die Tränen machten einem Lächeln Platz; radio has almost given way to television→ das Radio ist vom Fernsehen fast verdrängt worden

I'm not immediately able to see where you are going with the rest of your edit and I have to leave. I'll complete this answer later today. Could you please use complete sentences in your edit. It makes it difficult to see if your mistakes are intentional. A powder puff from the brand Trigwell is often seen in the hands of the cool girls with the smooth skin and I wondered whether they were on to something. Powder puffs aren't a recent invention but, you know what the internet is like; every now and then an influencer will 'discover' something for the first time and old things become new things. In these sentences the Gerund-Participle clause - driving my car - doesn't have an explicit subject. The subject is implicit - I. So naturally the structure of these sentence is not similar to that of the sentences in PART 1 of my answer. Therefore not comparable. I can do all things [which He has called me to do] through Him who strengthens and empowers me [to fulfill His purpose—I am self-sufficient in Christ’s sufficiency; I am ready for anything and equal to anything through Him who infuses me with inner strength and confident peace.]I didn't understand how omitting that just like your first sentence is relevant in the part after your "EDIT" in your question) These days, the jungle represents an unofficial post-Westminster payday. A sign that a political career is either flagging, dead, or, in Farage’s case, about to be resuscitated. For those “casting” the show, there’s now a “desperate/grubbing politician-type” slot to be filled. Elsewhere on the reality circuit, there’ve been similar manifestations, some more memorable than others. Ed Balls Gangnam Style-ing on Strictly Come Dancing; Penny Mordaunt belly-flopping in full hair and make-up on Splash!; George Galloway mewling like a pussycat for Rula Lenska on Celebrity Big Brother. While there’s been some public anger, including calls to boycott the show, the reaction seems oddly subdued. Nor, come to think of it, did there seem that much of a reaction when Boris Johnson (soon to join Farage on the GB News TV channel) was rumoured to be “in talks” for I’m A Celebrity himself. With Farage, there’s almost a sense of eerie inevitability (verging on surprise he hasn’t already been on). A shrugging, lifeless vibe of: “Yeah, this is what happens here. This is who we are now.” Call it what you will (viewer-fatigue; outrage-burn-out), there’s a perceptible cooling at the watercooler. Ellicott's Commentary for English Readers(13) I can do all things.--Properly, I have strength in all things, rather (according to the context) to bear than to do. But the universal extension of the maxim beyond the immediate occasion and context is not inadmissible. It represents the ultimate and ideal consciousness of the Christian. The first thing needful is to throw off mere self-sufficiency, to know our weakness and sin, and accept the salvation of God's free grace in Christ; the next, to find the "strength made perfect in weakness," and in that to be strong. It is not correct to say "...that gives human..." You are required to include an article or use the plural. "...that gives the/a human..." and "...that gives humans..." are all acceptable depending on what you wish to say.

In your case the subordinator that is omitted, and therefore your sentence #1 is incorrect, but your sentence #3 is correct. As I stride into the second half of my 30s, I've really noticed a change in my skin. I don't mind it in theory - laughter lines are a great privilege and crinkly eyes just show that you were happy. But I wouldn't mind looking airbrushed every now and again.

I'm not 100% certain of this but I believe that "that" can only be reliably omitted when the clause the begins with "that" is a noun clause and in the predicate (after the verb). give on to vi +prep obj (window)→ hinausgehen auf (+acc); (door)→ hinausführen auf (+acc); garden→ hinausführen in (+acc)