Suited is a bit more specific than suitable is.
To say that the property is suited for heuristic analysis would be to assume or imply that the property may have been build with that specific purpose in mind. To say that the property is suitable is to say that the property is able to be suited for heuristic analysis, but there's a chance some changes will need to be made.
Using 'applicable' in that context wouldn't make any logical sense.
As for the for/to statements, in that type of sentence I would use 'for'. Neither one is wrong though, they both make sense and nobody will question you. However if you want to get very specific, usually 'to' is used only when a an adjective or adverb is following. For example:
The property is suited for heuristic analysis.
The property is suited to his needs.
In context, you could replace the words "his needs" with "his use of heuristic analysis". I typed it the way that I did to more clearly show the point that I was making. Qualifying the statements by adding "than another property" is perfectly logical and would be entirely correct.
For the other question between applicability/suitability, applicability would make more sense, but both would be recognized and unquestioned. But I think there are better words that you could use, or maybe even just a better way of saying it. I'm having trouble of thinking of synonyms right now though, "usefulness" is the only word that comes to mind but even that really isn't much better.
However I do believe there are much better ways to say that. To say something like "I test this", or even if you used different words like "I check this", would be an incorrect form of participle in this context. To say that you test the applicability of the property would be to say that you do it often, say as if it's your job. So, if it's something you're currently doing or will do, then it would make more sense to say "I'm testing" or "I will test".
Given that I just changed both your verbs and direct object, you might as well change up those prepositional phrases as well to make it even easier to understand. The original "I test the applicability of a property for heuristic analysis" is just as correct, though it might linger in someones mind for a second longer (because 90% of people are stupid imo), and so it'd be better to just dumb it down some. Assuming you had a specific property in mind, you could actually make more sense by using the word I said no to, 'suitability', as long as you changed the entire rest of the sentence as I said.
I will test the suitability of this property for the use of heuristic analysis.
Obviously that's a lengthy sentence and would get in the way of a normal conversation, so here is where the use of English contractions and other forms of informal compressing become useful. Try it like this:
I'll test this property's suitability for heuristic analysis.
And there is how that sentence would be said in a normal conversation. Granted that you are from another culture, you might think that "informal" methods of compression like that are to be avoided in formal situations, but that's not what I mean by informal here. What I mean is that those rules or methods of compression aren't typically written or taught in length, they're just assumed when speaking. The only 'rule' that English culture has for formal speaking is to speak clearly and avoid all types of slang, which if you're a native English speaker, slang is very hard to avoid.
