In the context of the recitation of the Quran, Tajweed (Arabic: تجويد tajwīd) is a set of rules for the correct pronunciation of the letters with all their qualities and applying the various traditional methods of recitation (Qira'at).
It is Not necessary in Du'a and Dhikr to apply Tajweed rules, but we must recite Quran properly during Salah according to reading rules.
Yes, it is permissible to buy Quran with translation but you need to be sure about the accuracy of the translations as many translations available online and in book shops are wrong and misleading. Tajweed books and materials are always permissible.
Thank you for your question. There is no problem in buying these online.
May you always be successful.
Thank you for your question. Reciting whilst not knowing the rules of tajwid is not a sin, but a person should endeavour to pronounce the Arabic properly.
May you always be successful
You could make an agreement with yourself just to say each word once and keep going - you can always refine tajweed later. You could also try to pray in congregation more (insofar as it is possible).
I'm sure your tajweed is excellent! :)