Подальше DOES NOT necessarily mean "very far" or "far away", definitely doesn't mean "as far as you can" - that will be "как можно дальше".
It can mean a) a bit farther b) far enough away c) Really far away (but that usually used figuratively).
"Давай проедем подальше" does not mean let's drive as far as we
can, on the contrary it means "let's drive a little more (perhaps
looking for a parking spot and not quite ready to give up).
Similarly "Отойди подальше" does not mean "get away as far as you can", it
simply means "walk on a further". If the intonation is threatening it CAN imply something like "get the hell away from me (or it will get ugly)", but otherwise it's just a request to move a bit further. Plus if you really want to convey that you want them to move far away you'd say something like "Отойди-ка от меня подальше, повторяться не буду."
"Я бы так хотел уехать подальше отсюда" does indeed imply that you want to
get the hell away from here, as far as possible, however "Я переехал
подальше от работы" simply means that you moved and now you live
farther from work than you used to. It can be just a bit farther.
Basically подальше CAN mean "as far away as possible" (especially when used as a figure of speech, wishful thinking, etc.), but by far and large it just means "a bit further". Same way поближе just means "a bit closer", "closer than that even", it does not mean "as close as possible".
When using straight distance comparison between two things you сan for the most part use both forms, but подальше/поближе is a bit more colloquial.
"Её дом подальше моего" is fine, But to me "eё дом ещё дальше моего" sounds better, less folksy.
Подальше means "farther", while дальше сan mean both "farther" and "further".
You absolutely cannot say "Да, я и подальше собираюсь этим заниматься!" or "Он хочет в карьере пройти как можно подальше.". When you're not talking about some physical distance use дальше.
Дальше can also mean "go on" when asking someone to continue or simply "ok, let me continue/elaborate more" when you're about to continue.
"Так, значит продалжаю дальше, если никто не против."
It can also mean "after that" -
"А дальше там такое началось, что я не выдержал и уехал домой".
"Ну понял. А дальше?" - "Ok, got it, and then what?"
"Подальше" сan never be used in those cases.
If request to move something (or someone) farther or closer is repeated, you can say "подальше/поближе" the first time; but when you repeat it (needing more/less distance) you simply say "дальще/ближе", "ещё дальше/ближе" or simply "eщё"