From vVegetables to the zZoo

Correct title

Firstly, I need to buy vegetables and afterso that I can prepare lunch.

It is because you are buying vegetables in order to prepare lunch

To speak English, it's needed to understand grammar.

This makes sense but another way you could say this is "To speak English, I need to understand grammar" or "I need to understand grammar to speak English" or even "It's needed to understand grammar to speak English" Choose what you want :)

To get to the bus stop, you need firstly to goto go first toward the bookstore, and after thatthen toward the pharmacy.

I have an exam tomorrow, but I haven't learned the grammar for the test, so I need to cram my studying today.

Being more specific

On Saturday, my friend wants us to go to the pool, but another onefriend wants us to go to the zoo.

They cannot make a decision, so they told me that I have to choose.

Minor correction

From vegetables to the zoo

This is fine, but note that English tends to use title case for titles.

Firstly, I need to buy vegetables, and after that I can prepare lunch.

"First" would be more natural to me, but this is probably grammatical. Commas should have been used here, however.

To speak English, it's neededcessary to understand grammar.

But aAt the same time, it's not healthy.

Avoid starting sentences with "but," especially when not writing in a more literary style.

To get to the bus stop, you need to (firstly to?) go toward the bookstore, and after that toward the pharmacy.

This sounds more natural to me.

I have an exam tomorrow, but. Unfortunately, I haven't learned the grammar, so I need to cram today.

The original would be idiomatic when spoken informally, but having multiple coordinating conjunctions ("but," "so") in the same sentence (unless they're in parts separated by a semicolon) should be avoided.

They cannot make a decision, so they told me that I have to choose.

"Told" has to be followed by an object, typically the person to whom something is being told, sometimes a noun like "a lie" or "a story."

To speak English, it's needed toone must understand the grammar.

To get to the bus stop, you need firstly to go toward the bookstore, and after thatthen go towards the pharmacy.

I have an exam tomorrow, but I haven't learned the grammar, so I will need to cram today.

They cannot make a decision, so they told me that I have to choose.