There are only a few verbs which permit the bare infinitive (unmarked with to) in complementary non-finite clauses. These fall mostly into two classes (I’ve marked the absence of to with the conventional null symbol Ø):
causatives - have, help, let, make
I’ll have my assistant Ø send you the forms.
She helped him Ø correct his paper.
We cannot let this Ø happen.
The Devil made me Ø do it.
perceptives - feel, hear, see and others
He felt the wind Ø pick up.
I heard you Ø say it.
A witness saw him Ø shoot the deceased.
But most verbs, and all of those in your examples, require the marked infinitive (to-infinitive) in complementary clauses. (However, the to may be omitted by ellipsis when two or more infinitives are aligned in parallel, as in your last example: Just try to relax and Ø breathe. Here the to is implied before breathe, but need not be explicit.)
The bare infinitive is also used in questions with Why, with the full modal auxiliaries can/could, do/did, may/might, must, shall/should, will/would, and sometimes with the semi-modals dare and need.