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Of course it is.

Петенька, Петруша, Петечка, Петрунчик, Петрусик, Петюля, Петюня, Петруха, Петька

Just as it is written.

Definitions from my Oxford and Longman dictionaries:
cursive:
handwriting with letters rounded and joint together
script:
1) handwriting
2) printed cursive caracters in imitation of handwriting...

Лёнечка (affectionate)
Лёнчик, Лёнька (these are rather informal)

Write in script - пишите (or напишите) от руки

Probably it's because Alexey and Alexandr have a common nickname Alex. Maybe he called himself Alex and people thought that his name was Alexandr and not Alexey and so they called him Sashen'ka and...

Дочка is probably a little awkward (but possible), доченька is better, but it seems not very common to me, these words can be also used together with the name, for example:
Женечка, доченька, помоги...

As far as I know, it has no particular meaning, but people may have some weird reasons sometimes. Maybe there's a special story behind it. :) If it's not a secret, what is that person's full name?

I think "мама" is the most common. Also "мам" is common (which is sort of vocative case, it was mentioned here: http://masterrussian.net/mforum/viewtop ... 2675#12675 ) There's also "ма", but IMHO,...

What I wrote in brackets in my answer to BJ are just examples, you can replace any diminutive there with almost any other. And of course it's not necessary to use diminutives in these situations,...

Yes, it's quite normal.

It's quite normal if she introduces herself as Katya. The most formal form is a full name with patronimic (for example, Yekaterina Petrovna), this is the way the teacher would introduce herself to...

Галя (Galya) - a very common diminutive from Galina, but not the affectionate one.

affectionate diminutives:
Галечка (Galechka)
Галочка (Galochka)
Галенька (Galen'ka)
Галюша (Gal'usha)
Галюся...

http://masterrussian.net/mforum/viewtop ... olga#19037

"Could it be my voolga roostic speech?"[/quote]
Ha-ha, but that's 'vulgar rustic' in a thick North of England accent, has nothing to do with...