Sounds like regular maintanance problems not specific to the AE86. To fix all these problems would once have been called a "tune-up", an art now lost unless you read a book.
Ask the same question on American forums, the answer will be "get an ignition". By this they mean a huge MSD box. (Who would have thought the transister could make things larger?)
Others on this forum: "Ahhhrrr, the EVO misfiring system!"
Ask on Toymods: "Just save up for a 1UZ".
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