Je me suis levé à 10h h 30, j'ai pris un petit café au café Maison Polanski et j'ai acheté un kilo de pommes au marché.

lLa femmvendeuse me'a disait que c'était nommé une pirouette de pommes'elles se nommaient « pommes Pirouette », et je l’ai noté dans mes/sur mon bloc-notes danssur mon portable.

"femme" might sound slightly derogative in such a context
"Pirouette" is actually the variety. Fruit varieties are proper nouns and so, they're capitalized
Directly quoting a word or a specific term readers might not know => quotation marks
Apps, softwares, phones etc all require the preposition "sur" => sur mon téléphone, sur Instagram, sur ma tablette...

J'allaise suis allé au musée Beaubourg avec Sandrine, Adeline, Baptiste et Anouk.

Main event of your narration, focus on consequences or the fact it's achieved => passé composé, "je suis allé"

On faisa quand même fait autre chose quand même.

On a vu une petite exposition [de/sur ?] Guerlain aux Champs-Élysées.

"de Guerlain" would imply Guerlain organized it; "sur Guerlain" would imply it was about Guerlain. Not sure which one you meant here

Après, Bashir est parti et on est allés au bar nous quatre.

When "on" stands for a definite group of people (basically a "nous"), it requires plural agreements with substantives, adjectives and past participles

Je me sens un peu coincé du cul entre les trois femmes en train de bavardanter.

"coincé du cul" is highly colloquial (well, it's even vulgar) and means "uptight" as a whole (just making sure you knew it)
When there's no complement after a present participle, it's usual to use an infinitive structure ("en train de bavarder"). The present participle isn't wrong, you can still find it in old titles and texts, but it's totally old-fashioned now

On a rigolé sans arrêt des gens qui sont [propres et bavard de draguer quelqu'un. ?]

I didn't understand the end: "people who are clean and talkative to hit on someone"?