Learn Swedish: Mekanikern skulle titta på punkteringen, men han var sjuk. - The mechanic was going to look at the flat tire, but he was sick.

To talk about a plan or intention that was in the future from a past perspective (the 'future in the past'), Swedish uses skulle plus the bare infinitive of the verb, which is titta here. Think of skulle as the past tense of ska (will / is going to).

Do I always need to use på after titta?

If you are specifying what someone is looking at, yes. Titta på is a fixed phrase meaning 'look at' or 'watch'. If you just said titta alone, it would imply the mechanic was going to look around generally, without a specific object.

Why is the definite form of mechanic mekanikern instead of adding a full -en ending?

Nouns ending in -er, especially professions like mekaniker or tekniker, usually just take an -n to form the definite 'the' version. Adding a full -en ending would create a clunky -eren sound, so Swedish drops the extra vowel.

Is punktering the normal way to say 'flat tire' in Swedish?