In a medium pot of boiling salted water, cook green beans and carrot until crisp-tender, 1 to 2 minutes. Add peas and corn during the last minute of cooking. Drain. Run under cold water; drain, dry well, and put in a bowl.
In a large skillet, heat 1 tablespoon oil over medium. Add onion; cook until soft, 5 to 7 minutes. Add squashes; cook until crisp-tender, about 3 minutes. Place in bowl with drained veggies; add rest of oil, vinegar, mustard, and tomatoes. Add salt and pepper; toss. Top with feta and almonds.