CPU 100% stress

First find out what's causing this 70-95% the first few minutes. Fix that, if possible.
Freezing while gaming can be a symptom of insufficient cooling. A new CPU won't help.

Along with Kees thoughts go run Speccy and check out the drive SMART values 01 and 07. If big numbers I see that cause the 100% CPU use. If you can share the WEB SPECCY then I'll look for other causes there.

A new CPU will not fix this. But by CPU I mean the computer chip itself. Some folk call the big box, the CPU.

Read how to share at https://www.piriform.com/docs/speccy/using-speccy/publishing-a-speccy-profile-to-the-web

When you first boot any OS, the first coupla minutes it'll be doing a lot of housekeeping. Running whatever startup programs you have, starting services, etc. Since it dies off after a few minutes, I wouldn't worry about it.

I agree with the others, heat is a likely issue. Have you run Core Temp? The program should list what the maximum allowable temperature is for your CPU.

One way to test if it's heat is to purposely push the CPU with Prime95. Fire up Core Temp, then Prime95. Watch to see if the temps go over the max. If so, that's a sign of poor cooling. If they stay below but the machine locks up anyway, that's a sign that the CPU could be damaged.

Have you ever cleaned out the heat sink? Back when I didn't check, I have had a heat sink become completely impacted, where no air was flowing through the radiator fins. Is this a laptop or a desktop? If it's a desktop, it's usually easy to get at the heat sink to blow out the dust. With a laptop, you'll need to look up a YouTube video on the steps necessary to get at it. Most require removing 20-30 screws, often removing the keyboard, sometimes removing the monitor. And, sometimes the only way to get at the clogged radiator is to remove the entire heat sink assembly, which means you'll want some CPU heat transfer compound.

Also, since your machine is seven years old, the problem could be the heat compound has dried up. Possibly, reapplying that will help. Again, look up How-to videos. It doesn't take any fancy techniques. A pea-sized dab will do you.

Do you have a GPU? That's another component that can become clogged with dust. It also uses heat transfer compound. Look up your model on how to open it up. It's usually just a few screws.

In all cases, when blowing out the dust, do not allow the fan to spin freely. It is possible to over-spin the fan and damage the bearing. Also, might as well double-check that all your fans are actually running when you turn the machine on.

Just being thorough. Other slightly less common culprits for lockups are bad RAM or a flaky power supply. For RAM, boot up and run a memory test program. You might try just re-seating the RAM. And, you can try testing with less than the full complement of RAM. Depending on your motherboard, you can try different combinations or isolate each stick. For the power supply, I don't know of any easy test other than buying a new one and swapping it out.

For the stuttering, have you ever reinstalled Windows since you got the machines? The newer versions of Windows suffer far less Windows Rot than earlier versions. But seven years is a long time. It might be worth your time to back everything up and wipe it and reinstall. Up to you how much annoyance the stuttering causes.