There are definitely rattlesnakes in the park, but as has been mentioned, the dispersed camping area has a lot of activity and the snakes probably avoid it. The snakes actually come out when it is warm, so you don't have to worry about them as much at night. I was there for five days and did not see or hear a snake. I saw no ticks and very few other insects.

Always a possibility, but it's rather barren for ticks and many animals which carry them. The rattlesnakes are nearby, but the area is pretty well travelled and they don't like being around you anymore than you want to be around them. You'll have a bigger issue if you hike anywhere, however. Now will say, you don't need to be outside much, a ton to see traveling into the Joshua Tree Park roads. They have more descriptive plaques than any park I've traveled on - which is worldwide. In fact, I traveled a few days then and going back in 2 weeks for a longer stay. No more risk of pests than any campground and I actually think less so.

I only saw kangaroo rats.

I've only seen Desert Tortoise when hiking in the desert there. There are ants of many species but it depends on the time of year.

I did not see any snakes and there is not much brush for ticks to inhabit.

I was just there this weekend and usually go between January and March before it gets too hot. I've never seen either and I have two dogs so I inspect them regularly for signs.

I was there in November during a shoulder month. I saw neither. It was still mild/cold and windy cooling things down more. I imagine in hotter months this could be a potential issue.