We typically use 'we' instead of 'w' if the following word starts with a group of consonants the first one being either 'w' or 'f'. Hence 'we wtorek, 'we wrześniu', but 'w walizce' (second letter is a vowel).

Additionally we also use 'we' in front of the pronoun 'mnie' and a few other words which would be awkward to pronounce otherwise ('we dwoje', 'we Lwowie' etc.)

No.

'We wtorek' = 'on Tuesday'

'robię' = 'I make / I do / I'm making/ I'm doing'

'obiad' = 'lunch'

Well, you need to say what exactly is wrong, if you want us to react somehow. I don't see any mistake.

Locative is "wtorku", which would be visible in "We are talking about Tuesday" = "Rozmawiamy o wtorku".

For days of the week the construction is an exception and uses Accusative, actually. Same for the word "weekend". So for the masculine ones it will look the same as Nominative.

No. "we wtorek" means "on Tuesday", seperating them makes the sentence lose any meaning. Like "On I make lunch Tuesday".