[RadioKid]

1. NAKYA

"なきゃ:NA-KYA" is shortened form of "なければ:NA-KERE-BA" meaning "should not be" by itself. Combined with some behaviour, it means "Should" because there is hidden (or omitted) "can not be accepted".

I mean "NA-KYA" is shortened form of "NA-KERE-BA (NARANAI)" which has hidden part "NARANAI" meaning "can not be accepted".

"勉強しなきゃ:BENKYO SHI-NAKYA; must start studying" has omitted part "いけない” to mean "勉強しなきゃいけない：BENKYO SHINAKYA IKENAI; I can not accept not starting studying".

"NAKYA" itself means "unless" when used in "こんなに急ぎでなきゃ" meaning "unless in such case of hurrying".

2. MO

"MO" is often used meaning "too". In this case, he did something other than taking care of the house. And also, "MO" can be used meaning "even" ( "even taking care of ..." in this case).

3. KENDO

It can be typo of "しといたんだけど:SHITOITA-N-DA-KEDO;I had done it up”.

Another possibility is a dialect of northern Japan of "だけんど" meaning just same as "だけど" in standard Japanese.

Anyway, Japanese conversation often ends with "けど:KEDO;... but..." meaning ".... but are there anything wrong ?".

"しといた:SHITOITA;I had done" is shortened form of "しておいた:SHITE-OITA" in conversatin.