Ne quis ad fornicem vetustum accedat, dum faber tegulas mutat.

Because ne quis is a very common way in Latin to express a negative command of the type let no one... or may no one....

So:

• ne = negative particle used with certain kinds of commands/wishes
• quis = anyone / someone

Together, ne quis accedat means something like:

• Let no one approach
• No one is to approach
• No one should come near

A learner might expect nemo, but ne quis is especially natural in this kind of prohibitive or jussive expression.

After words like ne, Latin often uses quis instead of aliquis.

This is a standard pattern:

• aliquis = someone, anyone
• but after si, nisi, num, ne, Latin usually prefers quis

So ne quis is the expected form, not ne aliquis.

Here accedat is a present subjunctive used in a jussive sense.

A jussive subjunctive gives an exhortation, order, or command, especially in the third person:

• accedat = let him/her approach
• ne ... accedat = let him/her not approach

Since the subject is quis (anyone), the whole clause means:

• Let no one approach
• No one should approach

So the subjunctive is not showing uncertainty here; it is showing a command or prohibition.

Latin certainly has nemo meaning no one, but in this sentence the structure is specifically a prohibition:

• ne quis accedat = let no one approach

That is the idiomatic way to form this kind of negative command.
A plain nemo is more natural in straightforward statements such as:

• nemo adest = no one is here

So ne quis accedat is not just no one approaches, but rather no one must approach.

fornicem vetustum is accusative singular.

That is because it follows the preposition ad, and ad takes the accusative when it means to, toward, up to.

So:

• ad = to / toward
• fornicem = accusative singular of fornix
• vetustum = accusative singular adjective agreeing with fornicem

Together:

• ad fornicem vetustum = toward the old archway / old vault / old structure

The basic meaning of fornix is arch, vault, or arched structure.

Depending on context, it can also refer to a vaulted passage or similar structure. In some texts it can even mean brothel, because such places were associated with arches or vaulted rooms. But in this sentence, especially with roof tiles being changed, the architectural sense is clearly the one intended.

So here fornicem vetustum means something like:

• the old arch
• the old vaulted structure
• the old archway

Latin adjectives can come either before or after the noun, much more freely than in English.

So:

• fornicem vetustum
• vetustum fornicem

would both mean the old arch / old structure.

Here vetustum simply agrees with fornicem in:

• gender: masculine
• number: singular
• case: accusative

Word order in Latin often reflects style or emphasis more than strict grammar.

Yes, accedere already means to approach / go near, but Latin often adds ad with the accusative to make the goal explicit.

So:

• accedere = to approach
• ad fornicem accedere = to approach the arch / go up to the arch

This is perfectly normal Latin. The ad phrase tells you exactly what is being approached.

Because dum here means while, introducing a simple time clause:

• dum faber tegulas mutat = while the workman is changing the tiles

With this meaning, Latin commonly uses the indicative.

So:

• dum = while
• mutat = he changes / is changing

The clause gives the time during which the prohibition applies.

The basic meaning of mutat is changes or alters, but in context it often means replaces.

Since tegulae are roofing tiles, tegulas mutat naturally suggests:

• is replacing the tiles
• is changing the roof tiles
• is working on the tiles

English often uses a more specific verb than Latin does in this kind of context.

Faber means craftsman, artisan, workman, or builder.

It is a broad word. The exact kind of worker depends on context. Since he is dealing with tegulae (tiles), here he is probably some kind of builder or roofer.

So faber in this sentence is best understood as:

• the workman
• the builder
• the repairman

Tegulae are tiles, especially roof tiles in Roman building contexts.

So:

• tegulas = accusative plural, tiles
• faber tegulas mutat = the workman is replacing the tiles

The presence of tegulae helps confirm that the sentence is about building repairs and safety.

Latin often uses the present subjunctive for a command and the present indicative for a contemporaneous action, even when English might phrase things a little differently.

So:

• ne quis ... accedat = let no one approach
• dum ... mutat = while ... is changing

This sounds natural in Latin as a standing warning: no one should approach during the time the work is going on.

It breaks down like this:

• Ne quis ... accedat = main clause, a negative command
• ad fornicem vetustum = prepositional phrase, telling what not to approach
• dum faber tegulas mutat = time clause, telling when the prohibition applies

So the structure is:

Let no one approach the old archway while the workman is replacing the tiles.

That is a very typical Latin pattern: a command first, then a phrase showing the target, then a subordinate clause giving the circumstances.