Your original question has not been correctly answered.
Yes, under a J-1 you are eligible to file an I-539 (electronically if you want) to change your Non-Immigrant Status to B2 and this is a straightforward application. Once you have filed the I-539 you are legally authorized to remain the USA pending the decision. If you leave the USA whilst waiting for the decision though your application is considered abandoned and you would have no automatic right of re-entry.
See this link: http://www.uscis.gov/portal/site/uscis/menuitem.5af9bb95919f35e66f614176543f6d1a/?vgnextoid=ac3d8424f8304110VgnVCM1000004718190aRCRD&vgnextchannel=9059d9808bcbd010VgnVCM100000d1f1d6a1RCRD
The paragraph posted by "canadian_wife" refers to the restriction in changing your Exchange Visa Category and NOT your non-immigrant status altogether. For example changing from a J-1 trainee to a J-1 teacher would be subject to that restriction. Admittedly, it could be worded less ambiguously.
As for your 2nd question, there is no explicit limitation on the number times in a given period you may enter the USA using the Visa Waiver Program having read the rules and indeed twice in one year would be by no means exceptional. However, it remains at the discretion of the Border Patrol as to whether a visitor might be abusing the program to live or work in the USA and they do reserve the right to refuse entry on that basis. I repeat though, twice in year is highly unlikely to arouse suspicion.
tpuiatti got a reaction from Brother Hesekiel in Can I change the J1 visa status to a B2 visitor visa?