Do I need a business visa for Ireland if I already have Standard Visitor visa for UK?

UK visit visas issued prior to April 2015 were segmented along the lines of 'business', 'family', 'academic' and so on. The Immigration Act 2014 changed all of that and consolidated all visitor visas (which are technically known as 'entry clearances') into the single 'Standard Visitor Visa'...

This is the single consolidated UK visa type that covers all aspects where a person comes to the UK for tourism, visiting family/friends, job interviews, business trips, some forms of academic research, some forms of volunteer work, and group travel. It is uniformly multiple entry. This visa was created by the Immigration Act 2014 and has existed since April 2015. The 'Standard Visitor Visa' is a subset of the more generic UK 'entry clearance'.

(our tag definition for standard-visitor-visa)

On 20 March 2015, the Home Office sent an advisory to the UK legal community explaining the changes. Inexplicably, they did not put this advisory on the net, but here's a screen cap of the relevant portion...

So you can use your 10 year entry clearance for any permitted activity listed in Appendix V of the Immigration Rules.

In your case you can use your family visit visa to attend a business conference. Note that the reverse case (a business visitor wanting to engage in tourist activities) is already taken up in this site's archives.

See also: Entering UK for leisure while holding a business visa

For the other part of your question, Ireland is not in the UK or the Commonwealth, but it is in the Common Travel Area (CTA) and this is an open border arrangement. If you use a UK entry clearance to move within the CTA, (Ireland, Isle of Man, Guernsey, and so on), it's assumed that you have a local visa valid for seven days. The same goes for anyone issued a visa by a CTA member who comes to the UK, 7 days, unless they have a visa issued by the ROI, and in that case it's 3 months.

So your visit to the ROI is limited to 7 days.

Note: In anticipation of future questions, let me add that a Standard Visitor Visa can also be used in place of a UK Transit Visa.

Note: regarding the part about emailing the policy team, they will not engage with people unless the person is authorised and qualified under Sections 84 and 85 of the Immigration and Asylum Act 1999. That's why people complain that their emails are "ignored" when they ask about the Standard Visitor Visa. Hence this question can only be answered here and other sites (like forums and Colin Yeo's site).