With "L'abbiamo fatta", the subject is a feminine "it", shown through "la", which requires the use of "fatta" instead of "fatto".
So, does the use of "benissimo" imply the subject is male here, and would "benissima" imply the subject is female? Or do not all present-perfect verbs (or whatever tense we're learning) conjugate to the object?
Also, can you conjoin the article "il" with verbs?
You are right on this, in part:
With the direct object pronoun the past participle has to adapt. la which is a direct object pronoun (female, 3. person singular) would change the past participle in "fatta".
La pipi? L'ho fatta nel letto
A very often used sentence in Italian is:
Alla fine ce l'ho fatta. = Finally, I did it!
The part of your reflections on the word "benissimo" is incorrect.
benissimo is an adverb and so it hasn't to change.
It's one of the very little group of irregular adverbs (adjective: buono; adverb: bene, greater degree of comparison: benissimo) Adverbs could be compared but not inflected.
If you use "il" with a verb (infinitve) it becomes a subject (nominalization), you cannot use "il" to express "it". In the case above you have to use the direct object pronoun. (fare cq = direct object pronoun; fare cq a qc = direct and indirect object pronoun)
Il sapere è un bene garantito contro i rovesci della fortuna. (an example of nominalization)
With "fatto" after "avere", I don't believe actually change gender, I suppose because the act of "having" is an act, and not a description, so it doesn't need to agree with anything. With the verb "essere" on the other hand, you do change it with number and gender. So if you're female, you say "sono stata" while if you're male you say "sono stato" for example.
But aside from that, in this sentence the " L' " isn't even necessarily "la", it's equally acceptible for it to be "lo", which is the masculine equivalent (we're talking about pronouns here, "la" the article is a different case). Both "la" and "lo" are accusative "it"s, and since we don't know what the "it" is, we don't know whether the " L' " is masculine or feminine.
So just to be clear, "la" is both an article ("la pizza"="the pizza") and a direct object pronoun meaning "her", or "it" if the thing is feminine word: "La guardo" = "I watch her/it". With masculine these are different words: "il" is the article and "lo" is the direct object pronoun (though incidentally "lo" is used as an article in certain types of words that you probably know about, instead of "il").
in this case l' can only be "lo" because the past participle "fatto" isn't adapted as mtantillo said above.
A: ´Come ti piace la mia nave.
B: La nave è veramente bella, l'hai fatta benissimo!
you are right the past participle has to adapt with the auxilary "essere", BUT also with the auxiliary "avere" in case that direct object pronouns in the 3. person singular or plural (lo/la/li/le) are used (with the other direct object pronouns (mi/ti/vi/ci) it can be used but it's not obligatory and nearly never used).