however, therefore, furthermore (linking ideas) (B2 Grammar)

In formal writing, however links two ideas that pull against each other. The second idea is a surprise or the opposite of what the first one led you to expect. It's the formal cousin of "but" (which you'd use in speech). Form: it starts a new sentence with a comma after it — ...hard. However, he failed. — or follows a semicolon — ...hard; however, he failed. Don't glue the two ideas together with only a comma.

however: the other side

therefore: because of that

therefore links a cause to its result. The second idea is what follows from the first. It's the formal cousin of "so"; other words with this job: thus, consequently, as a result. Form: like however, it opens a new sentence with a comma after it — ...costs. Therefore, we... — or follows a semicolon. A comma alone before it is a comma splice.

furthermore: one more point

Furthermore adds a second, separate point that pushes the same idea further. It doesn't contrast and it doesn't show a result — it simply says "and here's more." It's the formal cousin of "and" or "what's more"; moreover and in addition do the same job. Form: it opens a new sentence with a comma after it — ...experience. Furthermore, she... — or follows a semicolon. Don't link the two ideas with only a comma.

as long as = only if; in case = as a precaution

As long as sets a condition that must be true: it happens only if that stays true. In case is a precaution: you do something now because something might happen later. They are not interchangeable.