It is prohibited to make images of live creatures. Jurists mentioned lots of narrated texts on this particular issue in their derivation books.
There is no problem in writing it to refer to the Besmalah, but the laws pertaining to the actual Besmalah, like the prohibition of touching it without the state of ablution, are not applicable to it.
Some of the narrations indicate that some of the main characteristics that should be sought in a spouse are good ethical values and religiousness. The religious appearances like having a beard and performing the prayers, and the observance of hijab for a woman, may not be sufficient indications to prove that. Therefore, one should make sure that these two characteristic exist.
<p style="text-align: left;">Yes, it is permissible to do so.</p>