If Alice and Bob share a Bell state, can Alice send her individual qubit to a third party?

Suppose Alice wants to send Bob information. Each of them has been sent each of the qubits of the Bell state in advance. Suppose Alice has the first qubit and Bob has the second.

$$|\Phi^+\rangle = \frac{1}{\sqrt2} (|00\rangle + |11\rangle)$$

Reference: Dense Coding Topic
QUANTUM COMPUTING
From Linear Algebra to Physical Realizations
Mikio Nakahara

Q1) What are the individual qubits received by Alice and Bob? Q2) If Alice wants to send her first qubit to Charles then is it possible to send her individual qubit? (or is it required to send complete $$|\Phi^+\rangle$$?)

Q1) The qubits in the $$|\Phi^+\rangle$$ state are entangled - this means that (by definition) you can not represent the state of one of them individually without talking about the second one (mathematically this would be represented as tensor product of two single-qubit states). The best description of the individual qubits received by Alice and Bob is that each of them is part of this pair; this specifies their behavior when measured or transformed in the best possible way.
Q2) Note though that the entangled qubits remain separate entities, stored in separate physical objects. This means that they can be sent around (for example, as photons) individually. So Alice can send her qubit to Charles without also sending him the second part of the $$|\Phi^+\rangle$$.