If a gentile wishes to sincerely serve God can they keep mitzvot like wearing Tallit or taffilin
A gentile may put on tefillin or tzitzit however he may not keep Shabbos or study torah. The proper way for a gentile to serve G-d is by keeping the 7 Noahide mitzvot properly. If he truly wishes to serve G-d on higher level he can convert to Judaism, which has numerous conditions, but as long as he remain a gentile these are his rules.
Rambam -Milachim 10-9,10.