When will my Lightning channel be closed? I have a force closed channel from lnbig.com and it has been pending in closing state for over 2 weeks (42600+ blocks). 
When might it be closed so I can request a new one?
What are the default/average values for different channel closing types?
Is there any way for me to check force close wait period?
When might it be closed so I can request a new one?


The time in which the transaction will be confirmed will depend on the fees of the last signed commitment transaction of your channel. the person force closing submits the last signed commitment transaction so as to get back the balance that is owed to them. You would need to monitor that transaction that was submitted by LNBig to the Bitcoin network to check for the fees. You can do so by searching with your funding transaction txid and any block explorer website will be able to show you the child transaction that consumes that output.  However, according to the BOLTs, the fees of the commitment transactions are always large enough for the transaction to get confirmed quickly.


  Is there any way for me to check force close wait period?


As said earlier, the force close wait period would depend on the fees of the last signed commitment transaction. If you had used C-lightning or LND implementations, it would have captured this transaction submitted. You can check whether the funds were returned to your wallet.


  I have a force closed channel from lnbig.com and it has been pending in closing state for over 2 weeks (42600+ blocks).


Just to get things straight, Bitcoin network generates blocks on an average interval of 10 minutes, which should correspond to about 144 blocks a day. Using two weeks time that is 2016 blocks. Since it's little more than 2 weeks, about 2200 blocks have been generated since it was closed. I think 42,600 blocks that you are mentioning is since the time the channel was opened way back in April.