To answer the numbered questions:
On a Unix or Unix-like system:
1: Feel free to fopen() anything you want. Other processes appending to the file won't be screwed up. Other processes moving the file won't be screwed up. Other processes deleting the file won't be screwed up. Their operations will continue to succeed, as will yours.
2: Reading the file won't prevent writers from writing, unless the filesystem is applying mandatory file locking. This is very unlikely, as it is a large performance penalty. (See your system's fcntl(2) manpage for details on mandatory locking.)
3: The scripts writing to the logs will probably not run slower while you are reading the files. The file data and metadata will need to be brought into memory for writing or reading; the logging might even run (ever so slightly) faster if your search keeps the caches hot.
4: Haven't got a clue. :)
I can think of several possible approaches to solving this problem:
First, you could perform the search first and then reverse the results:
grep danger /var/log/messages | tac
The search won't go any faster, but reversing will, assuming your results are a small-enough subset of the entirety.
Second, you could break your log file into pieces periodically using dd(1)'s skip=BLOCKS parameter; by breaking the file into 10-megabyte chunks, reversing those once, and handling the remainder afresh each time, you can amortize the cost of reversing the file all throughout the day. Programming this correctly would require more effort, but the time savings might be worth it. It depends how often the queries need to be made.
Third, you could write your own moral equivalent of tail(1) -f that is stuffing each new line into a ring-buffer file backwards. You'd be overwriting previous lines as you go, but it sounds like your log rotation already limits the amount of data being returned. A 600 megabyte limit might be reasonable. Your queries could start at the most-recently-written-byte, read through to the end of the file, and then start over at the beginning of the file if not enough results were returned. This would probably require the most effort to get correct, but amortizes the cost of reversing the database through every single log write. (If the scripts writing to the logs are bursty, this might seriously compete with the scripts for disk bandwidth at peak usage.)