1. No, it depends, but mostly through banks one are nominee, while those through investment house mostly are direct account. One has to check with respectively banks or broker house, different party can use different mechanism. Generally, there are no aware of any special restriction.
Whether it is a direct or nonimee, the shares are yours so you entitle all the dividend, share right or whatever.

2. Yes, you can. But it depends on your online trading portal website operation. Mostly portal is accessible for 24 hours 7 days per week unless stated otherwise for maintenance period or etc issues. But again you have to check with them, different party can implement differently.

3. Yes, it will appear on your online website, so do have SMS notification service also. Again it depends on your online portal you are using.

4. Yes, mostly will check automatical when T+3 to see whether got money to set off before the share being forced sell or notify their client of the shortage. Again you need to check with respectively broking house to verify.

They don't have too many copy I suppose. As one shareholder (broking house) will be sent one copy of annual report only so they need to photocopy for you as they might have one copy only!