As a 1099 worker, you can fund IRAs (of whatever type) and set up a SEP IRA with larger contribution options.

I would roll it over so you have complete control over it. That way if you have a financial emergency then you can access it (with penalties) much easier than going through the plan administrator at your old company. Also, my dad is an accountant and told me that one of his clients once had a very hard time accessing an old 401K account after the company went bankrupt and there was no plan administrator to contact anymore. Of course, that scenario is pretty unlikely, but it just goes back to being able to have the money under your control.

You can't contribute to that employer plan anymore, because you aren't an employee. You can leave the money in it, or you can roll it over into an IRA. There are pros and cons for each option - but if you do decide to roll it into an IRA, make SURE you do it correctly, because if you don't it may be deemed a distribution and you may be subject to deferred taxes and penalties.

I have 401k with my current employer and have been contributing to it. I am resigning and moving to 1099 based work. What do I do now? Can I keep contributing (w/o any employer match) or do I have to wait until I get a regular job?
Can I not contribute and let the already accumulated amount slumber there? TIA.