Once you are approved it takes 2-3 months to start recieving regular payments. any back payments usually take 4-6 months before you recieve them.
yes you can still work and earn a limited amount. Click on this link for more info: <a target=_blank class=ftalternatingbarlinklarge href="http://ssa-custhelp.ssa.gov/cgi-bin/ssa.cfg/php/enduser/std_adp.php?p_faqid=317&p_created=959362523&p_sid=11oOf62j&p_accessibility=0&p_redirect=&p_lva=&p_sp=cF9zcmNoPTEmcF9zb3J0X2J5PSZwX2dyaWRzb3J0PSZwX3Jvd19jbnQ9MzUsMzUmcF9wcm9kcz0mcF9jYXRzPTEwNSw4OCZwX3B2PSZwX2N2PTIuODgmcF9zZWFyY2hfdHlwZT1hbnN3ZXJzLnNlYXJjaF9ubCZwX3BhZ2U9MQ**&p_li=&p_topview=1
">http://ssa-custhelp.ssa.gov/cg...Q**&p_li=&p_topview=1
</a>
Yes you can work (NOT full time) while trying to get approved if it's under the limit (see previous link) but it's going to be more difficult to prove your case.
I'm not sure what you mean by what kind of health insurance. Once you are on SSDI for 24 months, you get medicare, and if you are within the income limits you might qualify for medicaid too. Is that what you are asking?