Question 1.  

Is now a good time to amend soil?  

It depends on what you are amending your soil with. Good information on soil preparation can be found in WSU's website Gardening in Washington State:

http://gardening.wsu.edu/compost-and-mulch/

Question 2.

When should I thin and transplant strawberry plants?

It depends on the variety. Below are two publications that may be helpful.

Strawberries for the Northwest at http://extension.wsu.edu/skagit/wp-content/uploads/sites/29/2014/03/070408.pdf

Growing Small Fruits for the Home Garden” available on-line at https://pubs.wsu.edu/ or the Oregon State Extension publication EC1307 and “Growing Strawberries in Your Home Garden” at http://extension.oregonstate.edu/catalog/.

Question 3. Do leaf miners come from soil

Yes, they overwinter under host plants. Larvae pass to the pupal stage and appear as young adults in late April.

http://hortsense.cahnrs.wsu.edu/Public/FactsheetWeb.aspx?ProblemId=6032

Question 4.

Is Neem oil ok?

Taken from WSU Publication, "If he wanted to use an “organic” or less toxic material, I would recommend an insecticidal soap or neem oil product. Thorough coverage of infested plants is crucial in achieving success with these. Since this is a non-food crop, there are other non-organic, more toxic products that will also kill aphids effectively. Products containing acephate, cyfluthrin, or imidacloprid should provide good rose aphid control.

When selecting any pesticide product read the entire label, even though the print is much to small to make this easy. Make sure the pest is listed on the label. Make sure the type of crop or plant is listed on the label. Read and follow all precautions for that product’s safe use in your garden and landscape, whether the material is organic or non-organic. This will protect your garden from pests".   http://ext100.wsu.edu/gardentips/category/pesticides/

For a additional information, contact the King County Master Gardener Program directly at:  <personal data hidden>

Or visit their website at: http://extension.wsu.edu/king/gardening/mg/