What is the difference between unable and incapable and unsuitable and impossible ?Feel free to just provide example sentences.

Great question. Very subtle nuances of meanings there. I'll give it a go:

On a semantic level, the pair unable/incapable basically shares the same meaning.

To be precise, some say that
-unable suggests inability dictated by circumstances or momentum
While
-incapable suggests a complete inability

E.g.
I'll be unable to play football this week as I feel a bit under the weather (momentary condition)

I'm incapable of playing football cause I have no co-ordination (permanent condition)

Frankly, the difference is so subtle that in oral communication both can be used interchangeably (even in written text if you ask me).

However, if the semantic difference is pretty much nonexistent, the grammatical level is worth of a brief consideration.

'Unable' takes the infinitive form of a verb
(unable to play)

'Incapable of' takes the gerund of the verb (incapable of playing)

Now, unsuitable means not appropriate or suited

E.g. Tropical climate is unsuitable for polar bears.

Impossible can have various meanings:

1) Not able to occur
In this case it differs from incapable or unable because it is used only for inanimate objects, whereas the former are used on sentient beings.

E.g. An impossible quest

2) intractable or unreasonable person

E.g. She goes hysterical for nothing. Such an impossible woman!

I hope I made myself clear and clarified your doubts. If not, apologies :p Appreciate the effort haha