1. You can generally use "tabhair" for English "give", so you could say "thug mé m'fhoclóir di" in both of your examples.
In the sense of "hand something to someone" you could also use "sín" or "cuir": "sín/cuir chugam an foclóir, tá focal le cuardach agam".
In the sense of passing ownership, there is also the verb "bronn", but I think "tabhair" is better, "bronn" seems a bit ceremonious.
2. "To take hold of something" would generally be "beir ar rud": Rug sí ar an fhoclóir"; if you're talking about taking something from somebody, you could use "beir ó", or "tóg ó" or "bain de" or "glac ó": "Bhain sí díom an foclóir", "Thóg sí uaim an foclóir", "Rug sí an foclóir uaim".
In the sense of "steal", you can use the verb "goid", but also "tóg" or "beir":
"Bhris sí isteach i mo theach agus rug léi mo chuid giuirléidí go léir, agus mise ag obair."
For taking photos, usually "tóg" or "glac" are used.