Learn English – letter has been sent to office by yesterday

The overwhelming usage is applicable to. The google reports 67.5M hits for applicable to and 340K hits for applicable for. (Admittedly this not an exact gauge.) I find a similar disparity on the Ngram viewer. Applicable means relevant or appropriate, and when the subject under discussion applies directly to the person addressed, then applicable to is the phrasing of choice. Sometimes, however, the subject under discussion is relevant to the situation of the person addressed but not to person himself or herself. In that case, applicable for may be used. Here's an instance from Vicki Lansky's Divorce Book for Parents:

One rule of thumb is 25 percent of the noncustodial's take-home pay at the time of your divorce will go to child support. But only a professional can tell you whether this will be applicable for you.

So, generally speaking divorced parents who aren't living with their children (noncustodials) can expect to pay one-quarter of their salary to support their children. But both custodial and noncustodial parents may be reading the book, and the 25% rule isn't applicable directly to custodial parents, only to their noncustodial ex-spouses. So the author uses applicable for to include the situations of both types of divorced parents.

Yes it can. The grammar and syntax leave the semantic sense uncertain, left to context.

It is not the more precise way of speaking you suggest, which would be to say "I met with her yesterday" - that "with" provides us with the extra common parlance (but not actually sufficient semantic accuracy!) needed to determine which of two senses is more likely even without added context. You could still choose to interpret that sentence as "I met with her yesterday (for the first time)."

To completely eliminate semantic uncertainty, it has to be an elocution more like "I reconnected with her yesterday" or something else which proactively enumerates the number of meetings which have occurred as being equal to or greater than one.