GFCI lights have gone crazy
A couple things here.  

GFCI devices differ one from the other

I'd imagine that most of your GFCI receptacles are one brand/model, and then you have a few of another brand/model.  Expect differences between them, and to understand any particular one, you need read its documentation: which in practicality means yank it out, obtain its model number, and look it up on the Internet.  The "yank it out" part is not something a novice should undertake.  So if the lights on different units do different things, I really don't care.  What I'm looking for is: 


If you push TEST, the power is knocked out. 
If you push RESET, the power comes back.  
If I use a plug-in GFCI tester in a location that is grounded and supposed to have GFCI, a GFCI trips somewhere, knocks out power, and power comes back when I reset. 


It is forgivable if power doesn't come back because another GFCI also needs to be reset. 



Some things should not be on GFCI

This is a matter of "best practice", not safety.  So if you have someone out for another reason, have them fix these.  

Top of the list is refrigerators. That actually is a safety thing.  Suppose Person A makes lunch so they plug in a sandwich griddle. The GFCI trips. A can't figure it out and walks away.  Family goes out for dinner.  Next day, B is making breakfast, finds tripped GFCI, unplugs griddle and GFCI resets OK.  Ducky doo, right? The refrigerator has been off for 18 hours.  

Second is most hardwired loads, i.e. those that don't get near water.  Lights which are not in a shower are at the top of the hitlist. You don't want the room turning pitch black the moment the grill, curling iron or circular saw trips the GFCI, because now you have hot things or fast moving blades inches from your body and you can't see.  The only way to make that worse is to add zombies.  

Other things that don't need GFCI are other non-water appliances that are properly grounded: Range hoods, built-in microwaves, dryers ranges and ovens that have 4-wire connections and are actually grounded, etc.  

In fact, having GFCI protection on a washer right next to a 3-wire-connected dryer is a picture postcard example of bad priorities: the grounded washer was never a threat, and the 3-wire dryer is waiting to kill someone. It's like a "No Smoking" sign right next to an unmarked open pit. 

Other GFCIs should not be on GFCI.  If testing one GFCI knocks out power to another, the second GFCI is redundant and is not needed.  It doesn't do any direct harm, but it does the indirect harm of someone being tempted to rip out annoying GFCIs.   However, don't confuse GFCIs with AFCIs, they provide completely different protections.  GFCI stops electrocutions, AFCI stops house fires.  

As for mysteries on Chinese power strips, I don't try to solve those.  Consumer grade power strips have weak surge protection that is only designed to last 3 months to a year depending on how many surges you get.  The 2020 Electrical Code will require a "whole house surge suppressor" on new and remodel houses and panels, and these typically come from the same Tier 1 suppliers who make the panels themselves, such as Siemens, GE, Eaton etc., so the good stuff.