Pretty sure current chances for PhD are very slim right now, so curious about chances for Masters then PhD.

PROFILE:
Type of Undergrad: BS Elec Eng, 2nd major Econ from ~top 10-15 US overall
Undergrad GPA: 3.5 (3.6 Econ)
GRE: Not yet (pretty sure M will be in range)
Math Courses: Up to Calc 3
Econ Courses (undergrad-level): Micro, Macro, Econometrics, Corp Fin, Intl Trade, Econ Risk & Uncertainty, Labor, Intl Trade, Environmental
Other Courses: Lots of Engineering/EE classes
Letters of Recommendation: Would get from Masters
Research Experience: None
Teaching Experience: None
Research Interests: Not sure
SOP: Not yet
Applying to: LSE? Not sure, seeking advice

So main questions are:

1) Where to apply for masters?

LSE, places in US?

2) Should I be taking more advanced courses before or during masters (eg Real Analysis, Linear Alg, etc.)?

3) Given that I do very well in the masters, what PhD programs will be in range? Any chance at:

UChicago, Columbia, NYU, Northwestern, LSE, UIUC?