How to calculate strength for titanium wire

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Stress = Force / Area, and "tensile strength" really means "tensile stress".

You need to be careful with units (and some people would recommend always convert everything into "basic SI units" of meters and Pascals), but using MPa and mm conveniently gives the force in Newtons.

The cross section area of your thin wire is $3.14 \times 0.3 \times 0.3 \,/\, 4 = 0.07065$ square mm, so the force to snap the wire is $0.07065 \times 240 = 16.956$ Newtons, or a weight of $16.956 / 9.81 = 1.73$ Kg.

For the thicker wire the force is $4.8$ Kg.

Note these are only approximate. You want to have a safety factor of at least 2, and maybe as high as 5, so the safe weights might be more like 350 grams and 960 grams.

The best thing to do would be attach something weighing that amount to a bit of wire, handle it roughly (for example jerk the wire rather than picking it up carefully) and convince yourself it isn't going to break before you start creating your jewellery.