The photos tell me nothing about the quality of the thermal compound (it's not an adhesive; it's to transfer heat). They tell me only that the installer used too much, which I find is common in laptop installations. It's more about the consistency of the compound, how it feels.
But, I don't even need to touch the thermal compound to know. The issue is age. Your laptop is nine years old. The thermal compound has dried out and cannot adequately transfer heat away from the processor, and there may be dust inside the laptop and inside the fan and heat fins. So, your laptop is unable to adequately cool itself.
Perform a careful but thorough internal cleaning. Clean out dust. Depending upon how dirty the inside of the fan is, you may be able to clean it just with a can of compressed air and a brush, or you may want to disassemble it. The old Inspiron I recently opened had so much dirt and fluff in the fan and heat fins that it was best to disassemble the fan, thoroughly clean it and then reassemble it and seal the joints exactly as it was from the factory.
While you're in there, replace the CMOS battery. If it isn't dead, it soon will be. BIOS settings and date/time can't be saved without a functioning CMOS battery.
You'll need to completely remove the old thermal paste before applying fresh.
To clean off old thermal compound, Arctic makes an excellent product. For Canadian $10 I got a package containing a bottle of ArctiClean 1 and a bottle of ArctiClean 2, enough to do several computers. ArctiClean 1 emulsifies old paste. ArctiClean 2 purifies the surface, removing any cleaner residue.
To remove old thermal compound, you could instead use high-purity (over 90%) isopropyl alcohol. But, ArctiClean's kit works so well and is inexpensive, so go with that.
When removing old thermal compound, be careful not to let any bits fall onto board or components. If it's metallic, those stray bits could cause problems later.
Many recommend coffee filters for cleaning, but many types of coffee filters have varying amounts of lint. Ideally, you want a lint-free material, such as microfiber cloth.
For new thermal paste, Arctic MX-4 is a good choice for a beginner. It's non-metallic (unlike Arctic Silver and many others), so if you accidently get a bit on another component, it won't be a disaster. Check what application method Arctic recommends for your processor:
You should also remove the thermal pads, follow the same cleaning process as for the thermal compound areas, and apply new thermal pads. You'll need to measure or judge to get the right thickness, which could be 0.5mm, 1mm, 1.5mm, etc.
Follow the disassembly and reassembly steps in Dell's Owner's Manual
Look on YouTube for videos showing disassembly of your model. But, be cautious with them, as some use steps or methods that are not appropriate. Use the videos to add to your understanding of what to do, but follow the steps in Dell's manual.
Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. I know many people do such work without this, but it's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard.