Reddit mentions of Coleman Cooler| 16-Quart Portable Cooler |EZ-Clean Excursion Cooler Ideal for Picnics and Barbecues

You have a few options depending on the size of the items.

1. This will be the most insulative but isn't very big so only travel sized version of sunscreen and such would fit.
   
2. This or something similar is your next bet. For these types of coolers fill the extra space with water bottles, they can be cooled, frozen or room temperature, but the extra mass of water will help keep the inside of the cooler cool.
   
3. A portable fridge, like [this](https://www.amazon.com/Chefman-Portable-Personal-Capacity-Freon-Free/dp/B076X7HF7F/ref=mp_s_a_1_5?crid=1XYI8QOJ9TFA2&keywords=portable+refrigerator&qid=1554274730&s=gateway&sprefix=portable+ref&sr=8-5, same tip with water applies here.
   
   A few additional Notes: use a sun reflector for when your car is parked. Put the cooler box or bag in a shaded area, oftentimes it will be cooler under a seat or in the trunk. Lastly all the items I linked are just examples, I don't endorce any(except the hydroflask).

I use this $15 Coleman cooler. Just got back from a three day trip, 70 degree weather and it still has a bit of ice in it. Keep it out of the sun and closed.

i) They are large, but they aren't endless. You would only want to put one cooler in there, and something small enough where you can put your other things in as well. When I go car camping, I typically bring something like this with me to keep items that must be kept cold.

If you can fit everything in your bear box, along with two coolers, then yes, you can bring two, but I would recommend only bringing one. They appear to be a lot bigger than they are once you start putting things in.

ii) The lockers themselves will "lock" so a bear can't get into them, but as far as to prevent another human, no. You cannot put locks on them either. If a Ranger sees this they will cut the lock off immediately.

I've camped a ton of times in Yosemite and have never had anyone bother my stuff. That goes for camping items and camping food. By no means should you be worried about food going missing, unless of course you fail to leave the bear locker unlatched to wear a bear or another animal could get it open.

If for some crazy odd reason this does occur, there are markets located in the valley and one in Wawona near the Big Trees Lodge where you can buy items.

iii) No, those are too big, they won't fit. You need small ones like the one I linked above.

Again as mentioned, only put items that must be kept cold. I don't know what you plan on cooking while you are there, but the weather will be cold. Things like water, soda, beer, vegetables, fruit, etc should be left out (inside the bear locker of course) as temps will keep them cool enough.

Only things that can easily spoil like eggs, meat, milk, etc should be kept in the freezer.

Also try to keep things compact as Rob said. It will make your life easier. For instance if I make scrambled eggs. I scramble the eggs up at home and put them in an empty gatorade bottle. Easy to store and don't have to worry about the eggs breaking.

Just remember larger things like boxes take up a ton of space. It's better to use smaller flatter compact things. Of course things like chips and what not are hard to do, but if you can cut up peppers, onions, etc before leaving, they'll lay flat in a bag.