MLa mia mattina e il mio pomerrigio

In Italian we put the articles before the possessive adjectives and pronouns.
There are some exceptions, like family name (ex. Mia mamma, mio papà).

Quando lavoro da mia cascasa mia mi alzaro alle sei e mezza ora.

Sadly, I can’t give you a good explanation on why it’s “casa mia” instead of “la mia casa”, you have to trust me with this one, it’s used a lot.
The present tense of the verb “alzarsi” is “io mi alzo”.
You don’t need to specify that you are talking about an hour.

Lavoro nello mio studio per un 'ora.

Normally it’s “lo studio”, but when you use mio it’s “il mio studio”, so in + il = nel.
Remember that it’s “una ora”, so it gets the apostrophe, if it’s a male noun you don’t have to use it.

Prosssimaoi/in seguito faccio una passagiata con il mio cane, ascolto un podcast in italiano mentre sto camminando.

'Prossimo' when talking about time is only used with “giorno (+ all the days of the week by name), settimana, mese (+ all the months by name), anno”.
You are talking about your everyday, so you must use the present tense.

Piuù tardi la mattina piu lavoro nello studio e faccio esercizio, per esempio ciclismo.

If the second “più” was meant to be a “poi”, you don’t need to use it.
“Fare esercizio”, because you do some exercise, there is also the conjugation “mi esercito”, but it can also mean to exercise yourself in a language.

Il pomerriggio inizia con una doccia.

Poi a pranzo, mangio un tramezzino e delle carrote.

If you use the preposition “a”, it becomes “at lunch”; if you don’t use any preposition in becomes the verb “pranzare” (to eat lunch), and the other verb becomes a gerundio.
"Poi pranzo mangiando un tramezzino e delle carote".
I used 'delleì to keep the sense of vagueness.

Lavoro e ho moltoe riuinioni che faccio su Zoom.