Gutters overflowing!

You could be risking damage to the foundation. It depends if the bed is properly graded or not. If the bed is graded properly, the water will run away from the house and the foundation. If not, the water could run towards the house.

After a heavy rainfall, see if the foundation concrete close to the dirt looks wet. If it stays wet looking for long after the rest of the foundation has dried, it could mean that water is running towards the foundation.

If that's the case, you have 3 options:

1. Fix the gutter.
2. Regrade the bed.
3. Run the risk of your foundation possibly being affected.

If the water is coming up from below into the window wells you have a big problem. That issue means your basement is becoming a reverse swimming pool. Imagine taking a big concrete box and putting in in a lake right up to the edge of the box. Eventually many many problems will crop up that your window well issue is just the first warning of.

You are going need to take that water away from the house.

A sump pump will do it quickest and easiest, as long as the power doesn't go out during a storm (gee, somehow that seems like it might happen, plan on having it happen and take what ever measures you think necessary, like back up power for the sump pump).

Redirecting the gutter downspouts will do even better if the power does go out.

Grading the slope of the land around your house to drain away from your house in every direction will also help without power - possibly with buried plastic under the soil sloping away from the house as well as a sort of 'earth sheltered umbrella'.

Adding new better french drains around the building while performing the grading and redirecting the downspouts and adding a sump pump or two would be best of all.

But in the end, if none of the above work, I would recommend abandoning the basement entirely, filling it in with gravel and a sump pump as the water level in your soil will never allow you to have a safely dry basement.

I know one family who had to do this very thing, and was much happier knowing that their foundation wouldn't become a molding swimming pool slowly being crushed by the outside soil/water pressure. It required moving some of the HVAC and other utilities that were down there, and using the space under the floor only as a crawl space.