Plugins that cause white-blank outs on WordPress website

What can WordPress do about these plugins and what other plugin can I use to get updates on how many folks visit my site?

Those plugins (well, Jetpack at least) don’t do that on a WordPress install but it is happening to your installation. Let’s see if some troubleshooting can sort that out. Try these temporary steps.

1 – Deactivate all of your plugins, no exceptions.

Edit: skip this theme step, I see you are using Twenty Eleven and that should be fine.
2 – Switch your theme to Twenty Fifteen. These are only temporary steps and you can undo them later.
3 – Clear your browsers cache and cookies.
4 – Log in again and activate the Jetpack plugin.
5 – One at a time activate the other plugins till you have a problem (the white blank page).
6 – When that happens (hopefully it will not) you will need to locate the directory of the offending plugin and rename it to something else. Your ISP provider guy may be able to help you with that step but please inform him what plugin it was.
7 – Put your old theme back.

This process of elimination will let you find where the conflict is and help you get support to fix it. But we really need to know where the conflict on your setup is in order to help you.