So in this case (where two sets of data are given), the "full pictures" (i.e. our Venn Diagrams) are not shown. &there4 it's good to bear in mind the following three possible scenarios of Venn Diagrams involving two sets, in order for you to have a clearer picture of which scenario to apply for the various parts of the question:

Let R = {women who like roses} and C = {women who like candlelight dinners}.

Translating what's given in the question into geeky Set Language, we have:

• "In a group of 350 women he surveyed" ⇒ n(ξ) = 350
• "200 of them like roses" ⇒ n(R) = 200
• "230 of them like candlelight dinners" ⇒ n(C) = 230

• no. of "women who like both roses and candlelight dinners"
  = n(R ∩ C) → let this be m

• no. of "women who like neither roses nor candlelight dinners"
  = n( (R ∪ C)' ) → let this be n

You're spot-on in your initial check of:
n(R) + n(C) = 200 + 230 = 430 > n(ξ)
⇒ there MUST be an intersection
⇒ R ∩ C ≠ (we can rule out the Disjoint Scenario)

1. To illustrate what you've worked out in a Venn Diagram, in order for m to be minimum we should be looking at the usual Intersect Scenario (since the Subset Scenario actually maximizes R ∩ C)

   

   From the diagram it's clear that:
   200 − m + m + 230 − m + n = 350
   ⇒ m + n = 80
   ⇒ Min m = 80 (occurs when n = 0)

   ∴ smallest possible % of women who like both roses and candlelight dinners
   = (80/350) x 100% ≈ 22.9% (3 sig. fig.)

2. To maximize n, we're looking to maximize the shaded area (R ∪ C)' in the Venn Diagram.

   Hence we should be looking at the Subset Scenario, where like you said "those who don’t want dinners also don’t want roses":

   

   So max n
   = n(ξ) − n(R ∪ C)
   = n(ξ) − n(C)
   = 350 − 230
   = 120

   ∴ largest possible % of women who like neither roses nor candlelight dinners
   = (120/350) x 100% ≈ 34.3% (3 sig. fig.)

As for Miss Loi's set ... umm ... probably (R ∪ C)' heee ...

Anyway,
1) If all ladies who like roses like dinners as well, then intersection = 0 people (since set representing ladies who want roses is a subset of ladies who want dinners). However, then there will be 430 people. Hence minimum intersection=
430- 350=80. %tage= 22.8% (3 sig fig)

2) Assuming all ladies who don't want dinners also don't want roses, maximum number of ladies who don't want both= 350-230= 120.
%tage= 34.3% (3 sig fig)

So which set do you fall into? ;D