Does my chain need to be replaced because it has looped itself many times?
If it's just tangled, untangling it is fine, but if your derailleur has suffered there's a good chance your chain has too, which will weaken the chain. Laying it out on a flat surface, it should look flat once you've taken out the loops. 

If you've got twisted links, they're likely to snag on the derailleur or gears, possibly only under load. If you try to straighten them, they'll probably end up stiff, and will be weaker. I recently trashed a rear derailleur and definitely had to replace the chain. Some links were badly twisted, and even with those removed the remaining chain was fragile (I snapped it twice in 5km of gentle riding). One almost new chain in the bin. You may be lucky, or you may be in the same position.