Although I have been using Linux from live media for a long time ,ever since my Windows 7 system get infected by a zero boot Trojan about 3 years back, I have never installed it. Can I install packs to a persistent hard drive like drivers for WIFi for Trisquel on a persistent thumb drive or is this only possible if I install an OS onto either my old failing internal hard drive or a bootable external portable hard drive?

Welcome to the forum!

Running Linux off USB is certainly possible, with extras being installed on it. Have a look at this
http://www.howtogeek.com/howto/14912...b-flash-drive/

Since SSD are arriving cheaper and larger, and rotational drive prices are dropping fast, you can replace a smaller drive very economically these days. If you have a failing drive, I recommend that you simply watch for the right deal and replace it. Persist is not a problem you need to solve, if you have a hard drive to install onto and use for persistent home files.

PS. I like to use persistent home and application files even when I boot from CD/USB live images. You may or may not, but either way having that internal drive gives you a solid and dependable home for persistent data and lets you play with more things. (Databases, programming languages, games, whatever twists your cork that needs room.)

Since the internet is needed for an install, you won't find any extra wifi drivers on a disk install.

I suggest either using an ethernet connection or because wifi cards are cheap, getting a replacement wifi card.

You can also purchase external hard drives (FireWire, Thunderbolt, USB 3.x) for less than $100 (USD) at an office-supply store ... with multi-terabyte capacity!

Unlike memory-sticks (which are much slower at writing than reading), these units will perform at near-native speed. You can easily install Linux directly onto one and boot directly to it (or, access it through a virtual machine), leaving your Windows installation unchanged.

The Internet may NOT be needed for an install IF the install media contains the complete and current distribution. Using the live first gives you a chance to test and verify the module and packages needed to support the WIFI networking. I have seldom needed drivers installed for anything else that were not immediately detected. (Well, in the last ten years or so. We need not discuss the OLD days, they are not coming back.)