Hey there @PotatoPhan, welcome to the discourse! I am going to do my best to answer your question below, but much of it will depend on your gameplay style, because at the moment there isn’t a “you must do this to win” type of system, it is all a giant sandbox for you to have fun in.
Don’t play on normal mode much, but having 2-3 during the Goblin campaign is wise, afterwards, likely don’t need more than 2.
Depends on what you are doing. If you are building lots of stuff with stone items, might need more than one mason. Same idea goes for weaver, lots of rugs needed? As for the cook, I tend to have 2 once I get more than 15 or so Hearthlings, but it really depends on how many mouths you wish to feed.
As with a cook, this really depends on the number of citizens you have, and how much you are trying to grow. If you have just the 7 starting hearthlings, you likely only need 1 farmer to feed everyone. However, if you are trying to grow 10 full size tree farms, you are going to need more. It all depends on the scale you are looking for,
For specific building tips I am going to direct you to take a look at this thread:
If you have any specific building questions, try asking in that thread as many of the “pro-builders” have posted there.
Just for my knowledge, which homescreen are you talking about? Here on the Discourse? On the wiki? On the website?