Yes, you can. However, many landlords prefer to use a process server to serve their tenant. A knowledgeable process server is an inexpensive safeguard — it prevents your tenant from using improper service as a defense. Improper service occurs when your tenant was served incorrectly or not at all.
Eviction notices do not need to be notarized. Just the signature of the person initiating the action on behalf of the owner is required. If the tenant doesn't comply by the deadline, your next step is to file for their removal at your local courthouse. The court does require one or more documents to be notarized at that stage.
You have the option to either accept or refuse partial payments. While there are always exceptions, it is highly recommended not to accept anything but payment in full. The cons heavily outweigh the pros. Accepting a partial payment after serving a notice may be considered a waiver of the notice in some circumstances.
Your next step is to file a complaint to evict in your local courthouse. A process server or sheriff will deliver a copy of the complaint to your tenant. The court gives the tenant additional time to respond or vacate. If the deadline passes, the court will issue a Writ of Possession that authorizes the sheriff to physically remove your tenant.