If I put a bento box inside this thermal bag, would it keep my food warm?

Off course, Smilco Reusable Insulation Bag can keep food warm according to your method

Would these bags protect eye drops from heat?

Insulated bags are usually designed to keep warm or cold, while eye drops usually need to be stored in a suitable temperature environment to maintain their stability and effectiveness. Therefore, placing eye drops in a thermal bag may adversely affect their stability, as the insulating nature of the bag may allow the temperature to rise, thereby exposing the eye drops to high temperatures. Eye drops usually need to be stored in a dry, cool, and light-proof place to avoid being affected by sunlight and high temperature, so as to maintain their efficacy and safety. If you need to carry eye drops when going out or traveling, you can choose a waterproof, moisture-proof, sun-proof small box or condom to store eye drops, and put them in a dry, cool place to maintain their good quality and effectiveness . In short, eye drops need to be stored in a suitable environment to maintain their efficacy and safety. Although the thermal bag can keep warm, it is not recommended to put eye drops in it, so as not to be affected by the high temperature.

Would these work for repackaging dehydrated meals?

It is not possible to use the thermal insulation bag to directly contact the dehydrated food. The dehydrated food can be packaged in the thermal insulation bag to achieve the purpose of insulation.

Do you have to use with ice packs or can this hold temperature by itself if an item come from the freezer to be shipped?

Never tried shopping without ice packs. With it being perishable I do all I can to keep it cold. I put the ice packs in the envelope with my mason jar. I use these disposable 2x2 inch ice packs. Works great together.