You can't buy HP, but you can buy HIVE and turn it into HP by 'staking' it in a PowerUp operation, yes. And it will be there forever until you decide to withdraw it. Withdrawing it takes 13 weeks, so if you had 1300 HP, your withdrawal would be 100 HP for 13 weeks to get it all back.

Similarly, any HBD you buy and put into Savings would also be there forever until you decide to withdraw it. Withdrawals from Savings take 3 days, for any amount you specify. Then it becomes liquid again.