من عادتي أن أشارك صديقي الشطيرة.

It is an idiomatic expression meaning it is my habit to... or I usually....
Literally, من gives a sense like among or from, so من عادتي is roughly among my habits. In practice, though, it is best learned as a fixed expression that introduces a habitual action.

عادتي is عادة + ي, so it means my habit.
When a noun ending in ة takes a suffix, that ة is pronounced as t. So عادة becomes عادتي = ʿādatī.

After expressions like من عادتي, Arabic commonly uses أن + imperfect verb to mean to do something.
So أن أشارك means to share. Grammatically, أن makes the verb subjunctive; in fully vowelled Arabic, it would be أشاركَ, but in normal unvowelled writing it looks the same.

أشارك is the I form of the verb شارك.
It comes from the root ش ر ك, which has to do with sharing or participation. So أشارك can mean I share or I participate, depending on context.

Because Arabic does not always copy the English structure.
With شارك, the person involved can come directly after the verb, so صديقي means the person with whom the sharing happens. In English we say share the sandwich with my friend, but Arabic can express that without a separate word for with here.

This verb can be structured so that the person comes first and the thing being shared comes second: أشارك صديقي الشطيرة.
So the order is different from English. English prefers share the sandwich with my friend, while Arabic here is built more like share my friend the sandwich in form, even though that is not natural English.

Because صديقي is already definite.
The suffix ـي means my, so صديقي already means my friend. In Arabic, a noun with a possessive suffix does not take الـ.

Yes, in this sentence it functions as the first object/complement of أشارك.
But nouns attached to ياء المتكلم (my) do not show the case ending clearly in normal spelling, so صديقي looks the same here. That is why the accusative is understood from grammar, not from a visible ending.

As written, الشطيرة means the sandwich because of الـ.
If you wanted a sandwich, you would normally say شطيرةً in fully vowelled text, or just شطيرة in ordinary writing. So this sentence is talking about the sandwich, not a sandwich.

It describes a habit.
The phrase من عادتي makes that clear. Without it, أشارك صديقي الشطيرة could mean a general or present action depending on context, but من عادتي explicitly gives the sense of repeated behavior.

Yes, شطيرة is a normal MSA word for sandwich.
In everyday speech, many people also use borrowed forms like ساندويتش, depending on region and register. But شطيرة is perfectly good standard Arabic.