Grammatical purpose of changing 〜る to 〜な, and expressing "even"

Question

I have to translate the following for my intro Japanese class.

父は、少し、働きすぎなので、庭の花や木に水でもやって、リラックスした方がいいとおもいます。

I understand parts of the sentence, but not the sentence as a whole.

I think 父は、少し、働きすぎなので is My father works a little too much so. But, I don't understand why it's すぎな and not すぎる.

I think 庭の花や木に水でもやって is Someone gives water even to the garden flower and the tree (etc). I am not sure how the "even" should be though.

Finally, I think リラックスした方がいいとおもいます is I think it is better if he relaxes.

So my questions are

1. Why the な instead of a る on the first part?
2. How is the even placed in the second part?
3. How do all three parts form a logical sentence?

My best guess is My father works a little too hard so, since someone even gives water to the garden flower and the tree (etc), I think it is better if he relaxes.

Answer 1

1. 働きすぎ is a 名詞 which comes from verb 働き過ぎる(働く+過ぎる).
   eg 食べすぎ / 飲みすぎ / 太りすぎ (+ だ/です) デジタル大辞泉 verb+過ぎ

2. The でも is used to give examples. デジタル大辞泉(See meaning #2-3)

3. The subject for 庭の花や木に水でもやって is 父.
   

父は、少し、働きすぎなので、My father is a little overworked, so
庭の花や木に水でもやって　(I think he should spend time doing things like) watering trees or flowers in his garden
リラックスした方がいいとおもいます。I think he should relax