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Both 诡异 and 奇诡 are adjectives. The "strangeness" translation is incorrect. 诡异 is a commonly used word meaning "strange". It can be used both colloquially and in writing. The idiom "好诡异" you mentioned means "How strange it is!". 奇诡 is a formal word used exclusively in literatures. It is a stronger form of 诡异 and is usually reserved for things that are ...
Its best to use "先...然后(first...and then)" or "之后(after)...再" to describe a sequence of events one after another. 她先跟朋友打网球，然后再去吃饭。(She's going to play tennis with friends first(先), (然后)then she will eat. or 她跟朋友打完网球之后，再去吃饭。 or even shorter... 她跟朋友打完网球，再去吃饭。 notice the use of 打完, it means after she finishes tennis, instead of 打 which translate to after ...
Actually the second one is quite natural. 她跟朋友打网球以后，她去吃饭。 This is actually the most legit you can get for this case, otherwise you will have to alter the meaning of your sentence a bit. Like: 她在网球场和朋友约好了， 然后再去吃饭。 Which means, she had a plan to go to tennis with her friends, and then dinner.
儿 is Pekingese (beijing dialect), like "lah" in singlish (singapore english). https://en.wikipedia.org/wiki/Beijing_dialect https://en.wikipedia.org/wiki/Singlish#Lah in general, you don't need to write it; unless you want to impress readers that it's pekingese.
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