Welcome to the community Harvey 
Yes you’ll be able to top up your Monzo account from your bank card or by bank transfer / standing order.
Unfortunately this won’t be possible until the current accounts launch.
You only have to top up £100 when you first order the card, after that, the minimum top up by card is £10 but you can use a bank transfer to top up smaller / more precise amounts.
Yes you will, it’ll have all of the standard bank account functionality that you use with a bank like Natwest 
I’ve put together a list of the functionality that’ll be available here -