If your DVR,and pc has a fire wire aka IEEE port you should be able to plug it into your computer and have no need for any tuner cards, as for recording multiple shows at once it depends on mythTV and your DVR. If it doesn't let you record more than one you might be able to trade in your DVR for multiple boxes without DVR no point in using a DVR if you can record on your pc(this would either require multiple tuners or multiple IEEE ports). Also if your box doesn't have an IEEE port you can call your television provider and see if you can specially request one that does.
Note: not all boxes with IEEE ports are compatible with mythTV it would be best to see if you can test it before you spent the extra cash.