Can L2S spouse work in US for a few months for India company till he/she finds a new job in the US?
Or
Can L2 take long leave from his/her company while being employed and search for a job and then resign and join US job once that is offered?
Should be okay. You may have to report any income paid in India bank account in your IRS return ad worldwide income fir resident aliens is taxed if you ar deemed US tax resident.
No issues. L2 EAD is an u restricted employment and have not limitations.