Dear Student,
(a) Yes, anything for which cash/cheque is received, shall be added to Cash A/c. So yes, the amount of premium received shall be included in Cash and Cash Equivalents (to be shown under the Assets head of the Balance Sheet)
(b) For writing off share issue expenses from Securities Premium, the entry is to 'Debit the Securities Premium A/c' and 'Credit the Share Issue Expenses A/c'