That sort of budget can get you started in liquidations, but it would be a small load, especially looking at the genre you want to deal in.
This is just my own personal opinion, but I believe drop shipping is a desperate option. It's the option that people chase when they either can't afford to spend the time developing a real business, the option they choose when they don't have enough money to buy in bulk and so on!
It's the option that has the potential to cause you more drama simply because you don't have total control over your own business, and it's the option that usually provides you with the least opportunity to make money!
To answer your questions;
1. I see absolutely no reason why you couldn't be successful, but I don't know the market for those products at all well, and therefore couldn't really say whether or not it was a good idea.
That's a question that only you can answer through your own research.
2. Yes you can buy home decor items through some liquidators, those that carry those types of loads.
If you can narrow down for me the type of decor products we are talking about I'll try and suggest an option or two for you. For example.......are we looking at items like cushions and throw rugs or lamps and side tables, etc.