Are there any recognized retirement plans / IRA accounts that also allow me to trade in stocks/options

You can open a self-directed IRA with most any online discount broker.

Self-directed IRA is the answer to your question and that is the account type you need to ask different institutions about. Some will allow options trading as well and I have never had a problem with that in my own self-directed IRA

Yes, there are many banks/brokers/others that will let you rollover your 401(k) into an IRA including E-Trade.

Investapedia has decent guide to get you started and look at the important question of whether to roll into a normal or roth IRA.

Edit in response to comment:401(k)'s (and rarely seen IRAs through your job) are restricted by the company's chosen investments but IRAs outside the company's program typically have few restrictions. IRAs directly through banks/brokers almost always have the only the same restrictions as normal accounts at the firm except for withdrawls, of course.

E-Trade, for instance, markets "Choose from stocks, ETFs (exchange traded funds), bonds, and over 8,000 mutual funds." for their rollover IRAs. They likely allow options as well but talk to their sales reps and there will be extra paperwork as there is for options on all accounts.

When I left a job I would roll my 401-K into an IRA at Scottrade. That IRA was one that I opened myself,it was not offered to me by any employer. After opening that IRA, I could then request the manager of the 401-K to send me a check made out to Scottrade referencing the account I had with Scottrade. Once I got that check I took it to a Scottrade office and they deposited it into the IRA. With Scottrade, I was able to speculate in options once my balance got high enough ($10,000 I think it was). As the IRA was opened by me and not by any company that I worked for I was able to buy any security that had a ticker symbol. I was also able to buy a zero coupon bond. You should be able to do the same with any IRA that you open yourself.