The rate of growth depends on the amount and size of each transaction people are doing on it. There are methods of pruning or discarding spent transactions, but someone somewhere would have to keep it all.

The amount of transactions people are willing to do depends on the value each does, so some people think if bitcoin transactions are almost free some other people would "spam" the network with their "worthless" transactions, thus increasing/growing the size needlessly. So these people claim high fees should ensure only really valuable transactions happen on the network, and not for buying coffe/payment-processing.

So your other question, astronomical, completely otterly astronomical.

Which is why people invent https://byteball.org and others to solve these problems.