I write in Polish notation and have included fully infixed notation here also which indicates parsing order.
For every relevant logic simplification fails:
Simplifcation: $CpCqp$ or $\big(p\rightarrow(q\rightarrow p)\big)$
I have a proof that from Syllogism, Commutation, Conjunction-Out Left, and Conjunction-in I can deduce $CpCqp$, given detachment also. You may see the August 19th answer here for details.
Syllogism: $CCpqCCqrCpr$ or $\Big((p\rightarrow q)\rightarrow\big((q\rightarrow r)\rightarrow(p\rightarrow r)\big)\Big)$
Commutation: $CCpCqrCqCpr$ or $\Big(\big(p\rightarrow(q\rightarrow r)\big)\rightarrow\big(q\rightarrow(p\rightarrow r)\big)\Big)$
Conjunction-Out Left: $CKpqp$ or $\big((p\land q)\rightarrow p\big)$
Conjunction-In: $CpCqKpq$ or $\Big(p\rightarrow\big(q\rightarrow(p\land q)\big)\Big)$
I highly doubt relevant logics don't have $CCpqCCqrCpr$ or $CKpqp$ when the have a conjunction connective. Does $CpCqKpq$ not hold for some relevant logics, and $CCpCqrCqCpr$ not hold for others? Or do they both fail for all relevant logics? Or does only one of them not hold? If so, which one?
In (most) relevant logic Syllogism and Communitation are Theorems, but for the conjunctions theorems it all gets a bit complicated, in most $CKpqp$ and $CKpqq$ are theorems but $CpCqKpq$ is not.
Instead of $CpCqKpq$, $CKCpqCprCpKqr$ is a theorem (this is also a theorem in classical logic) but you could argue that the last is not an conjunction-in theorem at all.
To get a real conjunction in rule, most relevance logics add an inference rule $\dfrac{\vdash p \quad \vdash q} {\vdash Kpq}$ but this is an inference rule not a theorem.