I went out to buy chesse, some bread and vegtables (today?). I went out to buy chesse, some bread and vegtables (today?).

The sentence feels unfinished without saying when you bought these items.

I went out to buy chesese, some bread, and vegetables. I went out to buy cheese, bread, and vegetables.

I went out to buy some chesese, some bread, and vegetables. I went out to buy some cheese, bread, and vegetables.

some can be applied to all items, so you can move it to the front.

I went out to buy chesse, somesome cheese, bread and vegetables. I went out to buy some cheese, bread and vegetables.

or I went out to buy cheese, bread and vegetables.

AfterWhen I came back home, the first thinkg I did. was When I came back home, the first thing I did was

Or "When I got back home" "After I got (back) home"

After I came back home, the first think I did. was bake a cake for my birthday. After I came back home, the first think I did was bake a cake for my birthday.

After I came back home, the first thinkg I did. was bake a cake for my birthday. After I came back home, the first thing I did was bake a cake for my birthday.

The earlier sentence was not complete (it's an incomplete thought), so I combined it with the following sentence.

After I came backreturned home, the first thinkg I did was to bake a cake for my birthday. After I returned home, the first thing I did was to bake a cake for my birthday.

Happy Birthday!

I bakeding a cake for my birthday. baking a cake for my birthday.

continuing on from the last sentence

I baked a cake for my birthday. I baked a cake for my birthday.

(Can delete this if you combine with the earlier sentence)

I baked a cake for my birthday.

The previous sentence was a fragment so I made it complete by appending this one.

I celebrated it with my sister. I celebrated it with my sister.

I celebrated it with my sister. I celebrated it with my sister.

Tense issue (keep everything in the past)

I celebrated it with my sister. I celebrated it with my sister.

I also recieved many emails and carteds from my family and my friends. I also recieved many emails and cards from my family and friends.

"my family" implies that they are also your friends so you do not need to repeat it

I also recieived many emails and carteds from my family and my friends. I also received many emails and cards from my family and friends.

I also recieived many emails and carteds from my family and my friends. I also received many emails and cards from my family and my friends.

Spelling issues

I also recieived many email messages and carteds from my family and my friends. I also received many email messages and cards from my family and friends.

This day is the happibest day of my life. This day is the best day of my life.

"Happiest" is not wrong but "best" sounds and suits better here

This day is the happiest day of my life. This is the happiest day of my life.

Thisat day iwas the happiest day of my life. That day was the happiest day of my life.

Happy bBirthday Courageuse19to me. Happy Birthday to me.

We don't really wish our own selves a Happy Birthday. If we did, we probably wouldn't say it to ourselves in third person.