The Find Familiar spell states that:
While your familiar is within 100 feet of you, you
can communicate with it telepathically.
and
Your familiar acts independently of you, but it always
obeys your commands. In combat, it rolls its own
initiative and acts on its own turn. A familiar can’t
attack, but it can take other actions as normal.
None of the familiars in the Find Familiar list are capable of speaking, nor do they know languages. Nevertheless, they can understand your commands, and they can take actions like Help and Search which are largely language-driven actions.
Also, the description of the spell Telepathy
reads:
Until the spell ends, you and the target can
instantaneously share words, images, sounds, and
other sensory messages with one another through the
link, and the target recognizes you as the creature it
is communicating with. The spell enables a creature
with an Intelligence score of at least 1 to understand
the meaning of your words and take in the scope of any
sensory messages you send to it.
and Speak with Animals reads:
You gain the ability to comprehend and verbally
communicate with beasts for the duration. The
knowledge and awareness of many beasts is limited
by their intelligence, but at minimum, beasts can
give you information about nearby locations and
monsters, including whatever they can perceive or have
perceived within the past day. You might be able to
persuade a beast to perform a small favor for you, at the
DM’s discretion.
To what extent can a simple animal familiar gained through Find Familiar understand and communicate/converse with you? Does Find Familiar intrinsically include the capabilities under Telepathy and Speak with Animals as you interact with your familiar?
Best Answer
Your familiar understands you perfectly.
You've already quoted nearly all relevant text in your answer. Telepathy (within range) communicates without necessarily using words, but the target (with int >= 1) understands perfectly.
I think your confusion comes from when you state
There is simply no such thing. From the spell description:
and thus it's impossible for it to actually be a simple animal.