C'est l'hiver, mais le temps faiest assez chauddoux.

"faire" is only used with the dummy pronoun "il": "il fait chaud, froid, du soleil". If you have "le temps" as a subject, the verb you're looking for is "être"
"doux" ("mild") would be a better way to phrase it IMO, but "assez chaud" isn't wrong in itself

Je n'ai pas fait due veélo récemment, donc je dois mettre de l'air dansregonfler mes pneus avant jde vaispartir.

to inflate, to swell, to put air into something = gonfler
gonfler again = regonfler
The little prefix "re-" is a very French way of expressing actions happening again, it can be added to most verbs

Nous irallons commencer la balade à veélo chez moi, et ensuite nous allons prendre la piste cyclable posur 10 milles.

If you meant "we're going to" (close future), it's always "nous allons" (with "aller" in the present tense)
"sur" is very often used to indicate duration spans or an area something or someone covers; "pendant" would've been right to

SuivantEnsuite, nous allons prendfaire une pause à/dans un restaurant, et prendre un casse-croûte et peut -être une bière.

Then, afterwards = ensuite
"prendre une/sa pause" is rather used in a professional contexts - must be because employees are given a break as an opportunity to seize/take, I guess
However, here, "faire" is totally better

Après cela, nous allons encore prendre la piste cyclable jusqu'à ma maisonchez moi.

at someone's = chez quelqu'un
To come back home = revenir chez soi
Expressions using "house" to give locations will generally use the preposition "chez" in French