1/ Gender agreement : “quel” is considered to be a pronoun here, a “pronom interrogatif”; as “numéro” is a masculine singular noun and that the masculine form of this pronoun is “quel” you say “quel est…”. Notice that “quel” is also an “adjectif interrogatif” (Quel numéro avez-vous ? (not a question for asking telephone numbers this one)).
As “quelle” is the feminine singular pronoun and “adresse” is a feminine singular noun you must say “quelle est…”
There are two other forms, the plural ones : “quels” and “quelles”.

• Quels sont vos numéros de téléphone ?
• Quelles sont vos adresses ?

2/ The agreement for the “adjectif possessif” is made according to gender and number with the noun that it modifies, not the recipient. The correspondences are found in the table below (due to bonjour France).

The second part of your question is answered, as you’ve probably noticed already, by the red coloured text.

• Pierre a dit « J’ai pris mon image dans cette pile.».

For your last question about mon amour, since LPH already answered the other points: it’s just that this word doesn’t have a feminine version, like most of French nouns if you think about it: une table, un ordinateur, un amour. If you want to call your male friend a "table" for any reason, it’s not going to change the gender of the word.

It’s not the same as using mon before a feminine word when it starts with a vowel.

Un ami, un chéri => mon ami, mon chéri (male)

Une amie, une chérie => mon amie, ma chérie (female)

Un amour => mon amour (male and female)

Other "pet names" examples that have only one version : mon cœur, ma moitié, ma puce, mon canard…

As a side note, amour becomes feminine when plural: mes amours perdues, it’s an exception.

We say

Quelle est ton adresse

Because adresse starts with a vowel, so as to ease the prononciation (ta adresse is kind of hard to say) we say ton adresse.

Here are some other examples :

Not starting with a vowel : Ta table, ta place, ta famille, …

Starting with a vowel : Ton orange, ton araignée, ton utopie, …

Be careful of some exceptions such as ton histoire, because here the h is silent.