A non-finite clause might better be defined as a clause headed by a non-finite verbform: an infinitive or a participle. Such a clause by definition1 has no tense. It cannot be the main or matrix clause in a formal sentence, because a matrix clause must be headed by a finite verbform, which defines its Reference Time—the time you are talking about. (see the discussion of tense here.)
Consequently, non-finite clauses only appear in formal sentences as subordinate clauses. Their temporal reference is inferred from context. In most cases that temporal reference is to the Reference Time defined by the matrix clause:
To think this makes him more cheerful may be paraphrased as
That he thinks this makes him more cheerful or
When he thinks this it makes him more cheerful.
A non-finite perfect construction—one in which the HAVE component is cast as a non-finite verborm—works the same way. (Keep in mind that the tense of a perfect construction is expressed by the HAVE component which heads it: a present perfect signifies a present state, a past perfect signifies a past state. Those states, current at Reference Time, arise out of the prior eventuality mentioned by the past participle component.). The semantics of think make it sort of odd in this context, so let's look at do instead.
To have done this makes him more cheerful may be paraphrased as
That he has done this makes him more cheerful or
When he has done this it makes him more cheerful
In the right context, infinitive clauses (including infinitive perfects), readily bear a future reference. For instance:
To think this this will make him more cheerful tomorrow.
To have done this will make him more cheerful in his old age.
1 ‘by definition’ because an English non-finite verbform is defined as one which is not marked for tense. Note that tense here is used in the technical sense “morphologically marked temporal reference”; English has, in this sense, only two tenses, past and non-past.
The difference in your first pair, with try, is addressed here.
Try to VERB means “attempt to accomplish the action of VERB”.
I tried to open the door = I attempted to cause the door to become open.
If the attempt succeeds, the action of VERB is accomplished: the door is open. If the attempt fails, the action is not accomplished: the door is still closed.
Try VERBing means “perform the action of VERB to find out if it will accomplish some other purpose”.
I wanted to clear the smoke from the room, so I tried opening the door = I opened the door in order to clear the smoke from the room.
The action of VERB is presumed to be accomplished. If the attempt succeeds, the purpose is accomplished: the smoke is cleared. if the attempt fails, the action is accomplished but the purpose is not: although the door is open, the smoke remains.
In both of these, the clause with VERB is the complement of TRY. This is not the case with STOP: STOP only takes gerund complements. However, it may take an infinitival adjunct describing the reason for stopping:
I stopped seeing him = I ceased to see him; I no longer saw him.
I stopped to see him = I stopped in order to see him; I ceased doing what I was doing or I made a stop in my trip so that I might see him.
Best Answer
In your example
There is no real difference in meaning or nuance.
However, the usual expression is
since "all" and "together" is automatically implied and is redundant.