Dear Rabbi Simon.
My new landlord doesn’t allow for any nails to be fastened to the wall or the door post. Is it permissible to attach a mezuzah by glue (if I can find a mezuzah like that)?
Yes. Some mezuzah cases are sold with an adhesive strip on the surface which attaches to the doorpost. You may use this. You may also find that a judicious application of a product such as Blu Tack also does the job effectively.
Remember to make the berachah when you affix the mezuzot in place.
Rabbi Rashi Simon