Dispute about scrabble basic rules

Yes, that's perfectly fine. Just so you don't add two letters on the end of raj and then another vertical word. I'm not sure how you would score it though.

I had to Google the words on your dang Scrabble board. Would've been nice to know that your version of Scrabble is ... Polish? So? Are "gad" and "rajd" Polish words? That would be your answer. Otherwise, gad is a word in English. Rajd isn't an English word at least according to dictioanary.com.

Polish words yes

I believe you would add up all the points from both words made. When you add the vertical word and it also changes the original horizontal word, you get all the points from both words. I'm not arguing whether each word is legitimate. You'll have to look that up.