Search
C-s (which is bound to isearch-forward) and C-r (which is bound to isearch-backward) work the same as GNU Emacs, except that wrapped searches are not currently supported. And slow terminal incremental searches are not supported.
Nonincremental searches invoked by pressing C-s <RET> (which is bound to search-forward) and C-r <RET> (which is bound to search-backward) work the same as in GNU Emacs.
Word searches invoked by pressing C-s <RET> C-w (which is bound to word-search-forward) and C-r <RET> C-w (which is bound to word-search-backward) work the same as in GNU Emacs.
Regular expressions searches are invoked by pressing M-C-s or C-s with a prefix argument (both of which are bound to isearch-forward-regexp) and M-C-r or C-r with a prefix argument (both of which are bound to isearch-backward-regexp). These work the same as GNU Emacs.
Nonincremental regular expression searches are invoked by pressing M-C-s <RET> (which is bound to re-search-forward) and M-C-r <RET> (which is bound to re-search-backward); they work very similarly to GNU Emacs, except for the difference described above.
Tint Emacs behaves the same way as the default GNU Emacs behavior with respect to searching and case, except that the variable case-fold-search is not supported in Tint Emacs. If a search string or regular expression is all lower case, then case will be ignored.
Tint Emacs uses a different, though somewhat similar, syntax for regular expressions than GNU Emacs. See Carp Regular Expression Syntax. It should be relatively straight forward to write a parser for the GNU Emacs regular expression syntax if someone were so inclined.
Replacement
M-x replace-string works the same as the default GNU Emacs behavior except that the variable case-replace is not supported. replace-regexp works the same as the default GNU Emacs behavior except that replacements are constant and the variable case-replace is not supported.
Query replace is invoked by pressing M-% (which is bound to query-replace) and the regular expression version is invoked by pressing M-C-% (which is bound to query-replace-regexp). These both work the same as GNU Emacs, except that C-l does nothing.