לתחתית ולדופן יש אותו עובי.

Because Hebrew usually expresses possession with the pattern:

ל־ + possessor + יש + thing possessed

So the sentence is literally structured like:

To the bottom and to the side, there is the same thickness.

That is how Hebrew normally says the bottom and the side have the same thickness.

This is very common in Hebrew:

• יש לי ספר = I have a book
• literally: There is a book to me

So in your sentence, יש is not strange at all; it is the standard way to say have.

Here ל־ marks the possessor, not direction.

In many contexts, ל־ can mean to or for, but with יש it often means something like has when translated into English.

So:

• לתחתית יש... = the bottom has...
• לדופן יש... = the side has...

This is one of the first big differences English speakers notice: Hebrew does not usually say X has Y with a special verb like English does.

Hebrew normally repeats the preposition before each coordinated noun:

• לתחתית ולדופן not usually
• לתחתית והדופן

So this is standard Hebrew style. It works like:

• לאבא ולאמא = to dad and to mom
• בבית ובמשרד = in the house and in the office

Repeating the preposition makes the structure clear and natural.

Because ל־ and ה־ combine.

So:

• ל + התחתית becomes לתחתית
• ל + הדופן becomes לדופן

In pointed Hebrew, you would see the difference more clearly:

• לַתחתית
• לַדופן

But in normal unpointed writing, the ה disappears from the spelling.

So even though you see לתחתית and לדופן, they can still mean to the bottom and to the side.

Here it means the same.

That is a very common use of אותו / אותה / אותם / אותן before a noun:

• אותו יום = the same day
• אותה בעיה = the same problem
• אותו עובי = the same thickness

So in this sentence, אותו is not an object pronoun like him. It is acting like same.

Because אותו agrees with עובי, not with תחתית or דופן.

The thing being described as the same is עובי = thickness.
And עובי is a masculine singular noun.

So Hebrew says:

• אותו עובי = the same thickness

Even though:

• תחתית is feminine
• דופן is feminine

The agreement is with עובי, because that is the noun after אותו.

עובי means thickness.

It is a noun, not an adjective.
Compare:

• עבה = thick (adjective)
• עובי = thickness (noun)

So the sentence is talking about the property thickness, not saying directly that something is thick.

You can think of it as:

• יש אותו עובי = there is the same thickness rather than
• they are equally thick

In this kind of sentence:

• תחתית = bottom, base, or bottom part
• דופן = side, often more specifically side wall or wall of a container/object

So if the sentence is about a box, pot, bottle, container, machine part, etc., דופן often means the wall/side wall rather than just a general side.

Also, both nouns are feminine:

• התחתית
• הדופן

Because יש does not really agree like a normal verb here.

In possessive/existential sentences, יש stays the same:

• יש לי
• יש לך
• יש להם
• לתחתית ולדופן יש

It does not become plural just because there are two possessors.

What changes is the rest of the sentence, not יש itself.

A natural pronunciation is:

la-tachtit ve-la-dofen yesh oto ovi

A few notes:

• לתחתית is understood here as la-tachtit = to the bottom / to the base
• ולדופן is ve-la-dofen
• ח in תחתית is the throaty sound, like the ch in Scottish loch or German Bach
• אותו is o-TO
• עובי is O-vi

Yes. A few natural alternatives are:

• לתחתית ולדופן יש עובי זהה.
  = The bottom and the side have identical thickness.

• העובי של התחתית ושל הדופן זהה.
  = The thickness of the bottom and the side is identical.

Your original sentence, לתחתית ולדופן יש אותו עובי, is perfectly natural and clear. It just uses same thickness rather than identical thickness.