1: They're grammatically OK (depending on context) and have similar but not identical meanings. 2: Again, similar meanings but very subtle differences. Nothing strictly incorrect according to my judgement, but most are inefficiently worded - there's a better way to word them. To elaborate: 2a. This is gramaticallty inefficient but I would not be so stict as to say it's incorrect, although I would expect a good proportion of other teachers to say it's incorrect. 2b. This is less inefficient, but still a bit inefficient. But it's not strictly incorrect. 2c. This is even more efficient, but still not perfect. Not incorrect. 2d. This is even more efficient still. It's practically perfect. 3a: These are not a complete sentence - not even a complete fragmented sentences. They sounds very weird like this, but they could potentially be joined with other words / slotted into sentences, and made to work fine without changing these words. They have similar meanings but not identical. Nothing strictly gramatically wrong, but like I said, they are sets of words, not complete sentences - they generally should not exist by themselves. 4: Just like section 3 - they're all potentially fine in certain sentences but can not exist by themselves else that would be terribly incomplete grammar. They can all be technically acceptable worded like this, within the right sentences, but some are more efficiently worded than others, and they all have similar meanings but not identical.

Of all your phrases, only the following are unusable: 2a "the place in which for Tom to live in" (delete "in which") 3a "the restaurant to eat" (people don't eat restaurants) 4b "the restaurant in which for Tom to eat" ("in which Tom eats") Even though the others are grammatical, many are awkward due to dangling participles. It is better to allow your prepositions to have objects. That is why 1a is a better phrase than 1b, and 3b is better than 3c. 2b becomes a better sentence if you strike out "in": "the place for Tom to live" has the same meaning but sounds much better.

Here's a corrected version of the question. There are several questions below, using four basic noun phrases. I must thank you very much in advance. Some of these may be correct, but not mean what you think they mean. A B and C in all examples imply that the action they refer to is not actually happening, only that it is advisable or is planned. 1a. the place in which to live. = I advise you to live in this place. 1b. the place to live in. = similar to 1a 1c. The place to live. = similar, but simpler and more natural. 2a. the place in which for Tom to live. I think this is actually incorrect. "In which for . . . " does not seem like a possible construction in English. 2b. the place for Tom to live in. OK, slightly awkward with IN at the end.Meaning: Tom doesn't live here, but it would be a good place for him to live, or this is the place he is planning to live in.. 2c. the place for Tom to live. GOOD - similar to 2b 2d. the place where Tom lives. GOOD different meaning from a,b,c 3a. the restaurant to eat. Grammatically okay, but doesn't make sense. If you are a monster who can eat buildings, then you can eat a restaurant. 3b. the restaurant in which to eat. Good - you are adivsing, or planning on eating at this restaurant. 3c. the restaurant to eat in. Good, similar to b 4a. the restaurant for Tom to eat in. Grammatically okay, but it's a weird sentence. To me it implies that someone has been searching for a restaurant that would be good for Tom. They have concluded that this is the best choice. 4b. the restaurant in which for Tom to eat. BAD - again, "In which for" sounds like an impossible construction in English. 4c. the restaurant where Tom eats. GOOD - 4d. the restaurant where Tom had been eating for three years. GOOD - different tense 4e. the restaurant in which Tom eats. 4f. the restaurant which Tom eats in. E and F are Good - Tom actually eats in this restaurant.

I'm not sure of the context for some of these but in 1a, 1b, and 1c using "the" sounds odd. I would use "A place in which to live", etc. They would all have the same meaning but 1a would be very formal. 2a is not grammatically correct. It would have to be, "The place in which Tom lives" but this would be extremely formal. 3a is not correct - it sounds like you're going to eat the restaurant itself 4b is not correct - you can't use "for" and "which" together.