good evening here, here are the answers for your questions.
specially vs especially:
It is better to use especially in front of adjectives to emphasize them, although some people also use specially
• The cake was especially good.
• This part is especially interesting.
Use especially to say that something applies more to one thing or situation than to others
• Everyone loved it, especially the children.
• You should call first, especially if you're going to be late.
Especially never comes at the start of a sentence
• He loves fruit. He especially likes kiwis (NOT Especially he likes ...).
Use specially to say that something is done or made for a particular purpose
• I got this specially for you.
• specially designed equipment
I went to the bus station to wait for him is correct (first comes the place then the infinitive of purpose).