(2) And is it haram to eat food of any party like birthday or anniversary?
بسم الله الرحمن الرحيم
Yes, you may apply henna during your menses, it involves nothing wrong. It is baseless what some women think that if they apply henna their ghusl and wudhu will not be valid until the colour of the henna remains, rather their wudhu and ghusl will be valid even with the colour of henna as well. It is mentioned in Fatawa Hindiyah:
فی الجامع الصغیر: سئل ابو القاسم —— او المراۃ التی صبغت اصبعھا بالحناء او الصرام وا الصباغ قال: کل ذلک یجزیھم وضوءھم (الفتاوی الھندیۃ 1:54، مکتبہ اتحاد دیوبند)
(2) Celebrating birthday is the way of the non-Muslims; Muslims are allowed neither to celebrate it nor to visit such events. However, if one goes to such events by chance, then the food will not be called haram like pork and wine.
Allah knows Best!
Darul Uloom Deoband