To both questions the answer is simple.
Let me provide you with some ahadith, and make ur own conclusion out of it.
Firstly:
‘Purity is half of the faith.’ [Transmitted by Muslim. Summarized Sahih Muslim lil Albani H.120]
Secondly:
Without purity prayer is not permissible.
Abdullah bin Umar (RA) related that he heard the Messenger of Allah (SAW) saying: ‘Allah SWT does not accept the prayer which is performed without purity, and does not accept charity from the wealth which has been stolen from booty.’ [Transmitted by Muslim. The book of cleanliness, Chapter obligation of cleanliness for prayer.]
Thirdly:
No part of the body over which wudoo is to be performed should be left dry.
Anas (RA) relates: The messenger of Allah (SAW) noticed a person whose part of the body (over which wudoo is to be performed) to the extent of a nail was dry. The messenger of Allah (SAW) commanded the person to go and perform the wudoo completely. [Transmitted by Abu Dawood and Nisaai. Sahih Sunnan Abu Dawood lil Albani Vol 1, H 158]
So taken these ahadiths, the first two speaking for themselves, the third one especially has to be be looked at conciously. Wudoo is performed over parts of the body, which includes nails! Nailpolish is not a part of the human body. Hence it covers the body part over which ablution is to be performed and prohibits the water from reaching the body part that should be reached: the nail itself. So simply said: The nails should be cleaned with water, WITHOUT the nailpolish. Otherwise your wudoo is invalid. The same goes for make-up. For example mascara, covers your eyelashes. It prohibits the water from reaching them, thus you’re not performing ablution completely.
As for praying with nail-polish and make-up, yes it is permissible. Once I was told a very beautiful example: When you’re preparing for a meeting with somebody very important, you want to look your best. Don’t you? You won’t go and meet that person wearing your pyjamas and without brushing your teeth or washing your face. If we are prepared to put so much effort in meeting a HUMAN like that, why do we lack on that while meeting our Creator? Who is more important than HIM? Why do we look for excuses then?
Allah is Beautiful and He loves beauty, so you’re very welcome to look your best wearing make-up and nailpolish. As long as you’ve done a proper ablution beforehand. 
I hope this all makes sense, it does to me… If there is anything wrong I said may Allah forgive me. May Allah grant us more knowledge.