My car has no compression, and I most likely bent the valves. Can I swap out the engine head and be good? Or did the pistons get damaged too? Is there a way of telling without taking the whole engine apart?

No compression, car may have had valves bent by you and this is a difficult situation as you need to consider the following:

1. Mechanic Evaluation: The surest method of determining how badly your engine has been damaged is having an experienced mechanic evaluate it. This way, they will be able to conduct various tests and inspections that would help them identify the source of low pressure and whether any damage was done on pistons or valves.
2. Bent Valves: Bent valves are often indicated by low compression. Failure or slipping off of the timing belt or chain can make interference between valves and pistons resulting in bent valves. Replacing bent valves and sometimes cylinder head can revive engine performance in many instances.
3. Piston Damage: The possibility exists that the pistons might also be damaged if they were bent because they interfered with the said items. Cases of contact between valve-piston can leave dented pistols or even cracks on them. It is however only through these detailed examinations which in most cases require partial disassembling of the engine that one can determine whether or not there is piston damage.
4. Visual Inspection: In other situations, mechanics like doing visual inspection hence remove cylinder head to check for status of; valves, pistons and walls of cylinders. However, partial dismantling may not show full extent of piston problems especially if any harm has not been discovered yet.
5. Compression Test: Before taking apart an engine, it is prudent to do a compression test so as to gauge its overall state. For instance, such test can point out those cylinders with reduced pressure thus provide some clues about what has happened inside them. Nevertheless, its results will never show if pistons have been damaged at all.
6. Extent Of Repairing Required: Bent valve replacements may be needed after consultation with your mechanic who could also advice on possible fixing/cylinder head replacement while dealing with any sort of piston cracking in case it happened under his watch depending on damage level as well as your budget.
7. Preventive Measures: To avoid related problems hence the importance of maintaining and replacing your vehicle’s timing components (timing belt or chain) when necessary as recommended by the manufacturer.

Summing up, it may be possible to fix this problem by changing the entire engine head but a good mechanic has to examine it fully and check if the pistons are affected. How much dismantling is required for assessing piston damage can vary, but having a professional evaluation is always better when deciding on repair work that should be done.