Tying Sewage Ejector Pump Pipe to Horizonal stack

Hello, I have installed a Everbilt sewage ejector basin system in my crawlspace and I have a few questions.
1. I am planning to tie the ejector pipe into a double wye, where one side is the shower drain, other side is the ejector pipe, and the straight through is the vent. Should I long sweep directly into the double wye or should I go just above the wye and drop down into the wye? See photo below
https://imgur.com/1rTceTg
https://imgur.com/eYVRnU8
2. Where the heck does the check valve go? My ejector pipe goes up 3ft, over 4ft, up 7ft, then ties to the horizontal sewer(stack?)

My old basin that serviced only a washing machine had a vertical check valve as high up as possible and a p trap after that, but I am not sure that was done correctly. My new basin services washer, lav, bath, and toilet.

Thank You so much for your help

 

New basin/pit will not connect to an air gap. Septic pit will be sealed. It needs a real vent (to the roof usually).
https://rooterman.com/columbus-oh/w...me-child/assets/images/sewer-ejector-pump.jpg

 

Thanks Reach4 this is to tie into the existing waste/sewer not the vent system. The new bathroom and basin will have its own new vent

 

tie pump to the horizontal waste line by dumping into top (a wye on back with branch pointing up). Not on its side! check valve goes in the vertical coming off pump

 

I like to install a check valve on the horizontal when I have an option only because of the head pressure placed against the flapper causes undo stress on the pump

Also when servicing a check a lot of installers do not install a valve above the check so when disassembling a 4 check for example vertical waste /soil line is full and makes a mess of the work site

 

service valve I always put on What about putting the check up higher reducing head pressure?
I always thought a little head better than none.