It is possible by using the Advanced search. There you can write some keywords and the related Groups to look. But it is possible only for Groups that you have joined. I'm not aware if there are more possibilities for "Pro" accounts.
Yes, that is possible. There is a per-group setting to control the frequency of digest emails. There is an overview for all groups from which it can be set in a batch-like fashion:
Settings (upper right, in pop-up under your name) -> "Email Preferences" -> "Set the frequency of group digest emails".
Change the popup for one or more groups from "Daily ...
It is actually possible to join up to 100 groups on LinkedIn, according to this post from someone who has joined 55 groups. She explains in a video in her post that you can join 50 parent groups and 50 subgroups. I checked a few of the groups in your screenshot, and I found that the "Disruptive I.T." group is actually a subgroup of the "Re-invent I.T." ...
Found any easier way to do this.
Hover your mouse pointer over your name at top right corner
click on settings
Click on Group, Companies and Applications tab
Click on Set the frequency of group digest emails
Select the options for each of your group
Click Save Changes
Thanks Alex for the help too.