هاي فرشاية السنان تبعي، ومعجون السنان تبع اختي.

هاي means this.

Here it is used because فرشاية is a feminine noun, and هاي is the common feminine singular demonstrative in Levantine.

A quick comparison:

• هاي = this, feminine
• هاد = this, masculine

So:

• هاي فرشاية = this brush
• هاد معجون = this toothpaste

In real speech, demonstratives vary a bit by region, so you may also hear forms like هيدي.

In Levantine, just like in Arabic generally, the verb to be is usually omitted in the present tense.

So:

• هاي فرشاية السنان تبعي literally looks like this toothbrush mine
• but it means This is my toothbrush

This is completely normal. Arabic does not need a present-tense is in sentences like this.

This is a noun + noun structure, often called an iḍāfa or construct phrase.

It literally means:

• فرشاية = brush
• السنان = the teeth

So together:

• فرشاية السنان = brush of the teeth = toothbrush

The same pattern appears in:

• معجون السنان = paste of the teeth = toothpaste

A useful thing to notice:

• the first noun usually does not take ال
• the second noun can take ال

So فرشاية السنان is natural, while الفرشاية السنان would not be the normal structure here.

Yes. السنان means the teeth, and it corresponds to MSA الأسنان.

In Levantine, سنان is a very common colloquial word for teeth. So:

• Levantine: السنان
• MSA: الأسنان

Same basic meaning, but السنان sounds more natural in everyday spoken Levantine.

تبعي means mine or belonging to me.

It comes from تبع, a very common colloquial word used to show possession.

Some common forms are:

• تبعي = mine
• تبعك = yours
• تبعه = his
• تبعها = hers
• تبعنا = ours

So:

• فرشاية السنان تبعي = my toothbrush
• more literally: the toothbrush belonging to me

Because the speaker wants to say my sister's, not just hers.

• تبع اختي = belonging to my sister
• تبعها = hers

If the listener already knew exactly which female person you meant, تبعها could work. But تبع اختي is more explicit and clearer.

Also, when the possessor is a full noun phrase, you normally use:

• تبع + noun

So:

• تبع اختي
• تبع أخوي
• تبع أمي

Yes, absolutely.

You can say:

• هاي فرشاية السنان تبعي، وهاي معجون السنان تبع اختي

That would mean:

• This is my toothbrush, and this is my sister's toothpaste

In your original sentence, the second هاي is simply omitted because it is understood from context. That is very natural in Arabic.

In formal Arabic, you would write أختي.

In informal Levantine writing, people often simplify spelling and write closer to how they speak, so اختي is very common.

So:

• أختي = formal spelling
• اختي = common colloquial spelling

Both represent the same word here: my sister.

Yes, فرشاية is a very common colloquial Levantine word for brush.

Compare:

• Levantine: فرشاية
• MSA: فرشاة

So:

• فرشاية السنان = everyday colloquial Levantine
• فرشاة الأسنان = more formal / MSA

Both mean toothbrush, but the sentence you were given is clearly in spoken Levantine style.

No. It is a very common way, but not the only one.

Another common colloquial option is إلي / إلك / إلو after the noun phrase:

• هاي فرشاية السنان إلي = this toothbrush is mine

For the second part, you may also hear:

• معجون السنان لأختي

But be careful:

• لـ can sometimes sound like for rather than clearly belonging to
• تبع اختي is often clearer if you specifically mean ownership

So in this sentence, تبع is a very natural choice.

Because in Arabic, the conjunction و meaning and is normally written attached to the following word.

So:

• و + معجون becomes ومعجون

This is standard Arabic spelling, not something special about this sentence.