My nails are brittle and break easily. Would applying a base coat of clear polish help make them stronger or healthier?

Not unless you use a "base coat" that is specifically designed to strengthen nails. Nutra Nail and Sally Hansen make numerous products for this purpose. I prefer OPI or China Glaze and OPI makes a really good product called Nail Envy that has 5 different formulations to target specific nail problems.

Pure almond oil rubbed into the cuticles and over the nail helps.

When you put nail varnish on it weakens your nails as they are not exposed to the air. (same as when you have false nails on and when you have them removed your own nails are weaker.

yes, that would be a good idea, but covering your nails with the polish just covers the problem on the outside. The reason why your nails are breaking is because of the lack of necessary vitamins that help keep your nails and bones stronger. Here is actually a very good article on how to strengthen nail.
Check it out, hope it will help.
http://www.modamee.com/2009/11/02/how-to-strengthen-nails/

I had the same problem until I tried Sally Hansen Nail Essential vitamins.. it works.

If you use a nail strengthener, it will certainly do a quick fix, but you may have to identify what, in your diet, is missing that you have such a problem. You may need to eat more orange vegetables and fruit, and take calcium supplements. I would talk to your local health professional.

Sunflower seeds are supposed to be good for your nails. You can sprinkle them over your breakfast cereal.

No it wouldnt unless the nail polish specifically says it strengthens nails because if you just use any random clear coat it doesnt let the nails 'breath' so they end up weaker than they were. Also wearing coloured nail polish all the time weakens them and they turn yellow