If your neighbor has a grub problem he soon will have a mole problem. Grubs don't migrate very far from their origination fortunately.
Exterminators can spray for spiders,fleas and ticks in the yard but I'd use a landscape co. or do it yourself for the fire ants.
What kind of spiders are disturbing you?
The barrier spray applied to doorways doesn't really work. The spiders that get indoors this time of year are mostly wolf spiders and they are destined to die without prey or access to water. They are scary but harmless.
As I understand it, grub killer is best spread when the grubs(beetle larvae) are actively feeding but not mature enough to transform into beetles(when they stop feeding).
A bag of grub killer ought to have the instructions for you.

There is still time to apply grub killer to your lawn the new grubs are onlly an inch or so under the surface now. If you wait beyond another week or two they will be too far down for the grub control to be effective. Act very soon.

It would be nice,mhallam, if you would respond to those who have given you suggestions in your 2 postings.
If you are new to maintaining a yard you will find that beginning a dialogue will be more helpful than throwing out a rant full of questions hoping for a magic solution requiring the least amount of work and money.

You said you arrived in your new home during the drought,that your soil is poor and filled with construction debris. Now, you want to attack a grub problem you think you might have because your neighbor does.

If your soil is solid clay and hard as the cement in your driveway and your lawn is patchy and weedy, the least of your problems would be grubs that really need a friable soil to be able to move to feed on grass roots.
Rock-hard clay doesn't support much insect life.

There are no simple solutions when you begin with a compacted,new construction yard.