A: You can submit a new application after your current registration is cancelled. Although, if the USPTO rejected your specimens for the renewal, it will also reject them for the new application. I recommend working with a trademark attorney to ensure you have acceptable specimens.
A: The fee to file an application electronically is $225 or $275 depending on the filing status. You will also need to pay an attorney to file the application. The attorneys fees can vary, but will generally be less than $1000. The estimated time to complete a registration is 18 months. I recommend speaking with a US trademark attorney to plan out how to establish your trademark rights in the US.
A: A trademark attorney would need to review the trademark registration and your product to determine if your product infringes their trademark. Generally speaking, exact copying is not required to infringe a trademark. If a consumer would confuse your mark with the other, there can be infringement.