Yes, that is YOUR 401k not theirs, but they will obviously not match your contribution.

Generally speaking, once you leave the employ of the company who sponsors your 401(k) plan, you are no longer entitled to contribute to it, or to borrow against it.

There are a ton of self retirement savings plans that you can contribute to. Take some time, do some cost/benefit comparisons and roll your current 401 into a new plan, and then contribute to it.

No you can't, but what you can do is go to a local brokerage and open an account in "street name" (eg. Billy-Bob's Big Brokerage'n'Bank FBO Mr.Sensitive) and do a direct rollover into that account from the 401(k). That way you never have the money in your direct possession and you won't have to pay taxes & penalties. If you start a business, you may be permitted to make additional "tax-deferred" contributions, though there are some restrictions on "intermingling funds"...

Your other option is to leave it where it is, though you won't be able to make any more contributions to that specific account.

You can roll it into an IRA and make contributions. However, if you own a business there are even better options for retirement savings. You can shelter a lot more money. If you do start a business I'd open such an account. Talk to an accountant or CFP about it.