It can also be unlimited if the host limits the upload rate, such that the more data uploaded the slower the rate. Reasonable usage won't be affected, just the outliers.
It would be. It's unlimited space, not unlimited bandwidth to put things in that space.
I feel that's what CrashPlan does, over the last few years I've rarely gotten over 500 KB/s upstream, although with my LTE router I regularly get 4-5 MB/s.
As long as the integral of rate limiter tends to infinity, rather than something less, the storage is unlimited. It is not relevant how long it takes to get there.